<PAGE>   1

                                   FORM 10-Q
                       SECURITIES AND EXCHANGE COMMISSION
                            WASHINGTON, D.C.  20549

                   QUARTERLY REPORT UNDER SECTION 13 OR 15(d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934

               FOR THE QUARTERLY PERIOD ENDED SEPTEMBER 30, 1996

                         COMMISSION FILE NUMBER 0-14457


                  NATIONAL HOUSING PARTNERSHIP REALTY FUND III
                        (A MARYLAND LIMITED PARTNERSHIP)
             (Exact name of registrant as specified in its charter)



                 MARYLAND                            52-1394972
       (State or other jurisdiction               (I.R.S. Employer
    of incorporation or organization)            Identification No.)


                               8065 LEESBURG PIKE
                                   SUITE 400
                             VIENNA, VIRGINIA 22182
                    (Address of principal executive offices)
                                   (Zip Code)


                                 (703) 394-2400
              (Registrant's telephone number, including area code)

                                NOT APPLICABLE
              (Former name, former address and former fiscal year,
                         if changed since last report.)


Indicate by check mark whether the registrant (1) has filed all reports
required to be filed by Section 13 or 15(d) of the Securities Exchange Act of
1934 during the preceding 12 months (or for such shorter period that the
registrant was required to file such reports), and (2) has been subject to such
filing requirements for the past 90 days.

Yes   X         No
   -------         -------
<PAGE>   2
PART 1 - FINANCIAL INFORMATION
ITEM 1 - FINANCIAL STATEMENTS

                  NATIONAL HOUSING PARTNERSHIP REALTY FUND III
                        (A MARYLAND LIMITED PARTNERSHIP)
                        STATEMENTS OF FINANCIAL POSITION

<TABLE>
<CAPTION>
                                                             September 30,
                                                                 1996            December 31,
                                                             (Unaudited)             1995      
                                                             -----------         ------------  
                                         ASSETS
                                         ------

          <S>                                                   <C>                <C>
          Cash and cash equivalents                             $ 142,255          $ 164,374
          Investments in and advances to                                                    
           Local Limited Partnerships (Note 2)                      -                  -    
                                                                 --------           --------
                                                                $ 142,255          $ 164,374
                                                                 ========           ========
<CAPTION>
                        LIABILITIES AND PARTNERS' DEFICIT
                        ---------------------------------
          <S>                                                   <C>                <C>
          Liabilities:
           Administrative and reporting fee
             payable to General Partner (Note 3)                $ 512,175          $ 447,489
           Accrued expenses                                        30,000             41,710 
                                                                 --------           -------- 
                                                                  542,175            489,199
                                                                 --------           -------- 
          Partners' deficit:
           General Partner -- The National
             Housing Partnership (NHP)                            (99,249)           (98,498)
           Original Limited Partner --
             1133 Fifteenth Street Three
             Associates                                          (104,149)          (103,398)
           Other Limited Partners -- 11,500
             investment units                                    (196,522)          (122,929)
                                                                 --------           --------
                                                                 (399,920)          (324,825)
                                                                 --------           --------
                                                                $ 142,255          $ 164,374
                                                                 ========           ========
</TABLE>




                       See notes to financial statements.

                                      -1-
<PAGE>   3
                  NATIONAL HOUSING PARTNERSHIP REALTY FUND III
                        (A MARYLAND LIMITED PARTNERSHIP)
                            STATEMENTS OF OPERATIONS
                                  (UNAUDITED)

<TABLE>
<CAPTION>
                                                                 Three Months Ended            Nine Months Ended
                                                                     September 30,               September 30,      
                                                                -----------------------   --------------------------
                                                                   1996         1995          1996          1995
                                                                   ----         ----          ----          ----

                 <S>                                              <C>          <C>         <C>           <C>
                 REVENUES:
                     Distributions and repayments
                       received in excess of investment
                       in and advances to Local Limited
                       Partnerships                              $    -       $    -      $  18,362     $    -
                     Interest income                                1,567        1,413        7,628          3,597
                                                                   ------       ------      -------       --------

                                                                    1,567        1,413       25,990          3,597
                                                                   ------       ------      -------       --------
                 COSTS AND EXPENSES:
                     Administrative and reporting
                       fees to General Partner (Note 3)            21,562       21,562       64,686         64,686
                     Other operating expenses                      13,448       10,712       36,399         35,346
                                                                   ------       ------      -------       --------

                                                                   35,010       32,274      101,085       100,032
                                                                   ------       ------      -------       --------
                                                                                                                  
                 NET LOSS                                        $(33,443)    $(30,861)   $ (75,095)    $ (96,435)
                                                                  =======      =======     ========      ======== 

                 NET LOSS ASSIGNABLE TO
                   LIMITED PARTNERS                              $(32,775)    $(30,245)   $ (73,593)    $ (94,507)
                                                                  =======      =======     ========      ======== 
                 NET LOSS PER LIMITED
                   PARTNERSHIP INTEREST                          $     (3)    $     (3)   $      (6)    $      (8)
                                                                  =======      =======     ========      ======== 

</TABLE>




                       See notes to financial statements.

                                      -2-
<PAGE>   4
                  NATIONAL HOUSING PARTNERSHIP REALTY FUND III
                        (A MARYLAND LIMITED PARTNERSHIP)
                         STATEMENT OF PARTNER'S DEFICIT
                                  (UNAUDITED)



<TABLE>
<CAPTION>
                                                 The          1133
                                               National     Fifteenth
                                               Housing        Street        Other
                                             Partnership      Three        Limited
                                                (NHP)       Associates     Partners         Total
                                             -----------    ----------     --------         -----

   <S>                                       <C>            <C>            <C>             <C>
   Deficit at January 1, 1996                $(98,498)      $(103,398)    $(122,929)      $(324,825)

   Net loss -- nine months ended
    September 30, 1996                           (751)           (751)      (73,593)        (75,095)
                                              -------        --------      --------        --------  

   Deficit at September 30, 1996             $(99,249)      $(104,149)    $(196,522)      $(399,920)
                                              =======        ========      ========        ========  
   Percentage interest at
    September 30, 1996                              1%              1%           98%            100%
                                              =======        ========      ========        ======== 
                                                   (A)             (B)           (C)        
</TABLE>

   (A) General Partner
   (B) Original Limited Partner
   (C) Consists of 11,500 investments units of 0.008522% held by 919 investors





                       See notes to financial statements.

                                      -3-
<PAGE>   5
                  NATIONAL HOUSING PARTNERSHIP REALTY FUND III
                        (A MARYLAND LIMITED PARTNERSHIP)
                            STATEMENTS OF CASH FLOWS
                                  (UNAUDITED)


<TABLE>
<CAPTION>
                                                                                               Nine Months Ended
                                                                                                  September 30,           
                                                                                    ------------------------------------
                                                                                           1996                1995
                                                                                           ----                ----

 <S>                                                                                   <C>                     <C>
 CASH FLOWS FROM OPERATING ACTIVITIES:
    Distributions received in excess of investment in Local
      Limited Partnerships                                                              $  18,362             $      -
    Interest received                                                                       7,628                3,597 
    Operating expenses paid                                                               (48,109)             (41,678)
                                                                                         --------              ------- 

 Net cash used in operating activities                                                    (22,119)             (38,081)
                                                                                         --------              ------- 

 CASH AND CASH EQUIVALENTS, BEGINNING OF
  PERIOD                                                                                  164,374              176,583 
                                                                                         --------              ------- 
                                                                                                     
 CASH AND CASH EQUIVALENTS, END OF PERIOD                                                $142,255             $138,502
                                                                                         ========              ======= 

 RECONCILIATION OF NET LOSS TO NET CASH USED
  IN OPERATING ACTIVITIES:

 Net loss                                                                               $ (75,095)            $(96,435)
                                                                                         --------              ------- 

 Adjustments to reconcile net loss to net cash used in operating
  activities:
      Increase in administrative and reporting fees payable                                64,686               64,686 
      Decrease in other accrued expenses                                                  (11,710)              (6,332)
                                                                                         --------              ------- 

        Total Adjustments                                                                  52,976               58,354
                                                                                         --------              ------- 

      Net cash used in operating activities                                             $ (22,119)            $(38,081)
                                                                                         ========              ======= 
</TABLE>




                       See notes to financial statements.

                                      -4-
<PAGE>   6
                NATIONAL HOUSING PARTNERSHIP REALTY FUND III
                      (A MARYLAND LIMITED PARTNERSHIP)
                        NOTES TO FINANCIAL STATEMENTS




(1)      ACCOUNTING POLICIES

         ORGANIZATION

         National Housing Partnership Realty Fund III (the "Partnership") is a
         limited partnership organized under the laws of the State of Maryland
         under the Maryland Revised Uniform Limited Partnership Act on May 10,
         1985. The Partnership was formed for the purpose of raising capital by
         offering and selling limited partnership interests and then investing
         in limited partnerships ("Local Limited Partnerships"), each of which
         owns and operates an existing rental housing project which is financed
         and/or operated with one or more forms of rental assistance or
         financial assistance from the U.S. Department of Housing and Urban
         Development ("HUD").

         The General Partner raised capital for the Partnership by offering and
         selling to additional limited partners 11,500 investment units at a
         price of $1,000 per unit. The Partnership acquired limited partnership
         interests ranging from 94.5% to 99% in twelve Local Limited
         Partnerships, which were organized to directly or indirectly own and
         operate existing rental housing projects.

         BASIS OF PRESENTATION

         The accompanying unaudited interim financial statements reflect all
         adjustments which are, in the opinion of management, necessary for a
         fair statement of the financial condition and results of operations
         for the interim periods presented. All such adjustments are of a
         normal and recurring nature.

         While the General Partner believes that the disclosures presented are
         adequate to make the information not misleading, it is suggested that
         these financial statements be read in conjunction with the financial
         statements and notes included in NHP Realty Fund III's Annual Report
         filed in Form 10-K for the year ended December 31, 1995.

         The preparation of financial statements in conformity with generally
         accepted accounting principles requires management to make estimates
         and assumptions that affect the reported amounts of assets and
         liabilities and disclosure of contingent assets and liabilities at the
         date of the financial statements and the reported amounts of revenues
         and expenses during the reporting period. Actual results could differ
         from those estimates.






                                      -5-
<PAGE>   7
                  NATIONAL HOUSING PARTNERSHIP REALTY FUND III
                        (A MARYLAND LIMITED PARTNERSHIP)
                         NOTES TO FINANCIAL STATEMENTS


(2)      INVESTMENTS IN AND ADVANCES TO LOCAL LIMITED PARTNERSHIPS

         The Partnership owns a 99% limited partnership interest in Brunswick
         Village Limited Partnership and 94.5% limited partnership interests
         (98% with respect to allocation of losses) in nine other Local Limited
         Partnerships. The Partnership also acquired a 99% limited partnership
         interest in Meadowood Townhouses I Limited Partnership and Meadowood
         Townhouses III Limited Partnership. These two Local Limited
         Partnerships each own a 99% limited partnership interest in an
         operating limited partnership which holds title to one and two rental
         housing properties, respectively. The Partnership's effective interest
         in these operating limited partnerships is 98.01%.

         Because the Partnership, as a limited partner, does not exercise
         control over the activities of the Local Limited Partnerships in
         accordance with the partnership agreements, these investments in Local
         Limited Partnerships are accounted for using the equity method. Thus,
         the investments (and the advances made to the Local Limited
         Partnerships as discussed below) are carried at cost less the
         Partnership's share of the Local Limited Partnerships' losses and
         distributions.  However, because the Partnership is not legally liable
         for the obligations of the Local Limited Partnerships, and is not
         otherwise committed to provide additional support to them, it does not
         recognize losses once its investments, reduced for its share of losses
         and cash distributions, reach zero in each of the individual Local
         Limited Partnerships. As of September 30, 1996 and December 31, 1995,
         investments in all twelve Local Limited Partnerships had been reduced
         to zero. As a result, the Partnership did not recognize $977,447 and
         $948,615 of losses from these twelve Local Limited Partnerships during
         the nine months ended September 30, 1996 and 1995, respectively. As of
         September 30, 1996 and December 31, 1995, the Partnership has not
         recognized a total of $13,583,436 and $12,605,989, respectively, of
         its allocated share of cumulative losses from the Local Limited
         Partnerships in which its investment is zero.

         Advances made by the Partnership to the individual Local Limited
         Partnerships are considered part of the Partnership's investment in
         Local Limited Partnerships. When advances are made, they are charged
         to operations as a loss on investment in the Local Limited Partnership
         using previously unrecognized cumulative losses. As discussed above,
         due to the cumulative losses incurred by the Local Limited
         Partnerships, the aggregate balance of investments in and advances to
         Local Limited Partnerships has been reduced to zero at September 30,
         1996 and December 31, 1995. To the extent these advances are repaid by
         the Local Limited Partnerships in the future, the repayments will be
         credited as distribution and repayments received in excess of
         investment in Local Limited Partnerships. These advances are carried
         as a payable to the Partnership by the Local Limited Partnerships.





                                      -6-
<PAGE>   8
                  NATIONAL HOUSING PARTNERSHIP REALTY FUND III
                        (A MARYLAND LIMITED PARTNERSHIP)
                         NOTES TO FINANCIAL STATEMENTS



         No working capital advances or repayments occurred between the
         Partnership and the Local Limited Partnerships during the nine months
         ended September 30, 1996 and 1995. The combined amount carried as due
         to the Partnership by the Local Limited Partnerships was $538,469 as
         of September 30, 1996. Future advances made will be charged to
         operations; likewise, future repayments will be credited to
         operations.

         The following are combined statements of operations for the three
         months and nine months ended September 30, 1996 and 1995,
         respectively, of the Local Limited Partnerships in which the
         Partnership has invested. The statements are compiled from financial
         statements of the Local Limited Partnerships, prepared on the accrual
         basis of accounting, as supplied by the management agents of the
         projects, and are unaudited.

                       COMBINED STATEMENTS OF OPERATIONS

<TABLE>
<CAPTION>
                                         Three Months Ended                      Nine Months Ended
                                            September 30,                          September 30,         
                                --------------------------------------    ------------------------------------
                                     1996                1995                1996              1995
                                     ----                ----                ----              ----

 <S>                             <C>                <C>                   <C>                <C>
 Rental income                   $2,129,727         $ 2,099,539           $6,370,214         $6,393,190
 Other income                       108,627             102,900              275,705            259,905
                                  ---------           ---------            ---------          ---------

    Total income                  2,238,354           2,202,439            6,645,919          6,653,095
                                  ---------           ---------            ---------          ---------


 Operating expenses               1,549,288           1,573,398            4,464,866          4,501,045
 Interest, taxes and
  insurance                         693,742             725,995            2,172,399          2,185,986
 Depreciation                       346,573             312,658            1,003,562            931,887
                                  ---------           ---------            ---------          ---------

    Total expenses                2,589,603           2,612,051            7,640,827          7,618,918
                                  ---------           ---------            ---------          ---------

 Net loss                        $ (351,249)        $  (409,612)          $ (994,908)        $ (965,823)
                                  =========           =========            =========          =========
 National Housing
  Partnership Realty
  Fund III share of
   losses                        $ (346,021)        $  (402,812)          $ (977,447)        $ (948,615)
                                  =========           =========            =========          =========
</TABLE>




                                      -7-
<PAGE>   9
                  NATIONAL HOUSING PARTNERSHIP REALTY FUND III
                        (A MARYLAND LIMITED PARTNERSHIP)
                         NOTES TO FINANCIAL STATEMENTS


(3)      TRANSACTIONS WITH THE GENERAL PARTNER

         During the nine month periods ended September 30, 1996 and 1995, the
         Partnership accrued administrative and reporting fees payable to the
         General Partner in the amount of $64,686 for services provided to the
         Partnership. The Partnership has not made any payments to the General
         Partner for these fees during each of the respective periods. The
         amount of fees due the General Partner by the Partnership was $512,175
         and $447,489 at September 30, 1996 and December 31, 1995,
         respectively.

         The accrued administrative and reporting fees payable to the General
         Partner will be paid as cash flow permits or from proceeds generated
         from the sale or refinancing of one or more of the underlying
         properties of the Local Limited Partnerships.





                                      -8-
<PAGE>   10



ITEM 2 -         MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION
                 AND RESULTS OF OPERATIONS

                  NATIONAL HOUSING PARTNERSHIP REALTY FUND III
                        (A MARYLAND LIMITED PARTNERSHIP)



LIQUIDITY AND CAPITAL RESOURCES

The properties in which the Partnership has invested, through its investments
in the Local Limited Partnerships, receive one or more forms of assistance from
Federal, state or local governments or agencies. As a result, the Local Limited
Partnerships' ability to transfer funds either to the Partnership or among
themselves in the form of cash distributions, loans or advances is generally
restricted by these government-assistance programs. These restrictions,
however, are not expected to impact the Partnership's ability to meet its cash
obligations.

Net cash used in operations for the nine months ended September 30, 1996 was
$22,119 as compared to $38,081 for the nine months ended September 30, 1995.
The decrease in cash used in operations resulted primarily from an increase in
distributions received in excess of investment in Local Limited Partnerships
and an increase in interest income during the nine months ended September 30,
1996 compared to the nine months ended September 30, 1995.

No working capital advances or repayments occurred between the Partnership and
the Local Limited Partnerships during the nine months ended September 30, 1996
and 1995. The combined amount carried as due to the Partnership by the Local
Limited Partnerships was $538,469 as of September 30, 1996. Future advances
made will be charged to operations; likewise, future repayments will be
credited to operations.

Distributions received from Local Limited Partnerships represent the
Partnership's proportionate share of the excess cash available for distribution
from the Local Limited Partnerships. As a result of the use of the equity
method of accounting for the Partnership's investments, as of September 30,
1996, investments in all twelve Local Limited Partnerships had been reduced to
zero.  For these investments, cash distributions received are recorded in
income as distributions received in excess of investment in Local Limited
Partnerships. During the nine months ended September 30, 1996, cash
distributions of $18,362 were received from two Local Limited Partnerships.
There were no cash distributions during the nine months ended September 30,
1995. The receipt of distributions in future quarters is dependent upon the
operations of the underlying properties of the Local Limited Partnerships.

Cash and cash equivalents amounted to $142,255 at September 30, 1996. The
ability of the Partnership to meet its on-going cash requirements, in excess of
cash on hand at September 30, 1996, is dependent upon the future receipt of
distributions from the Local Limited Partnerships,





                                      -9-
<PAGE>   11
                  NATIONAL HOUSING PARTNERSHIP REALTY FUND III
                        (A MARYLAND LIMITED PARTNERSHIP)
          MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION
                           AND RESULTS OF OPERATIONS



General Partner advances, or proceeds from sales or refinancings of the
underlying properties of the Local Limited Partnerships.  Cash on hand at
September 30, 1996, plus any distributions from the underlying operations of
the combined Local Limited Partnerships is expected to adequately fund the
operations of the Partnership in the current year. However, there can be no
assurance that future distributions will be adequate to fund the operations
beyond the current year.

The Partnership currently owes the General Partner $512,175 for administrative
and reporting services performed. The payment of the unpaid administrative and
reporting fees will most likely result from the sale or refinancing of the
underlying properties of the Local Limited Partnerships, rather than through
recurring operations.

National Corporation for Housing Partnerships was a significant participant in
the drafting and passage of the Low Income Housing Preservation and Resident
Homeownership Act of 1990 ("LIHPRHA"). LIHPRHA creates a procedure under which
owners of properties assisted under the HUD Section 236 or 221(d)(3) program
may be eligible to receive financial incentives in return for agreeing to
extend their property's use as low income housing. The appropriation for the
Department of Housing and Urban Development (which administers LIHPRHA) for the
1997 fiscal year was recently approved and is insufficient to meet existing
program demand. As part of this appropriation, Congress directed HUD to suspend
processing of any property which had not received approval of a sale or
refinancing under LIHPRHA as of the date of enactment of the appropriation,
which occurred on September 26, 1996. Brunswick Village and Meadowood I, II and
III all received approval to be sold under the program within the requisite
timeframe; however, none have been allocated funds under the 1997 fiscal year
appropriation, which is required so that these transactions can close. It is
uncertain at this point whether LIHPRHA will receive future appropriations from
Congress sufficient to allow the sales of Brunswick Village and Meadowood I, II
and III to close. In the event that the LIHPRHA sales do not close, the General
Partner will investigate other sale or refinancing opportunities for these
properties, but there can be no assurance that these efforts will be
successful.  If unsuccessful, this could have a substantially negative impact
on the Partnership's future available capital resources.

All the Local Limited Partnerships in which the Partnership has invested carry
deferred acquisition notes due to the original owners of the Properties. In the
event of a default on these notes, the noteholders would assume ownership of
both the General Partner's and the Partnerships' interests in the Local Limited
Partnerships. All of the notes have final maturity dates between 1996 and 1999.
Due to the weakness in the rental markets where some of the Properties are
located, the General Partner currently believes the amounts due on the
acquisition notes may likely exceed the value to be obtained through the
Properties' participation in LIHPRHA or other sale or refinancing





                                      -10-
<PAGE>   12
                  NATIONAL HOUSING PARTNERSHIP REALTY FUND III
                        (A MARYLAND LIMITED PARTNERSHIP)
          MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION
                           AND RESULTS OF OPERATIONS



opportunities. In the event that the Partnership loses its interest in these
Local Limited Partnerships, the partners in the Partnership may incur adverse
tax consequences. The impact of the adverse tax consequences is dependent on
each partner's individual tax situation.

The former owners of Meadowood I, II and III hold deferred acquisition notes on
the three properties. The deferred acquisition notes related to Meadowood I and
II matured April 15, 1996, and are now in default, while the notes related to
Meadowood III will mature on April 15, 1997. However, the General Partner has
negotiated a forbearance agreement with the noteholders which permits the
Meadowood Local Limited Partnerships to participate in LIHPRHA as described
above. If LIHPRHA funding is not approved for fiscal year 1997, the forbearance
agreement provides that the noteholders will not  foreclose on the notes until
January 1998.

RESULTS OF OPERATIONS

The Partnership has invested as a limited partner in twelve Local Limited
Partnerships which operate thirteen rental housing properties. In prior years,
results of operations of NHP Realty Fund III were significantly impacted by the
Partnership's share of the losses of the Local Limited Partnerships. These
losses included depreciation and accrued interest on deferred acquisition notes
which are noncash in nature. Because the investments in and advances to Local
Limited Partnerships have been reduced to zero, the Partnership's share of the
operations of the Local Limited Partnerships is no longer being recorded.

The Partnership's net loss decreased to $75,095 for the nine months ended
September 30, 1996 from a net loss of $96,435 for the nine months ended
September 30, 1995. Net loss per unit of limited partnership interest decreased
from $8 to $6 for the 11,500 units outstanding throughout both periods. The
decrease in net loss was primarily due to an increase in distributions and
repayments received in excess of investment in and advances to Local Limited
Partnerships, and an increase in interest income. The Partnership did not
recognize $977,447 of its allocated share of losses from the twelve Local
Limited Partnerships for the nine months ended September 30, 1996, as the
Partnership's net carrying basis in these Partnerships had been reduced to
zero. The Partnership's share of losses from the Local Limited Partnerships, if
not limited to its investment account balance, would have increased $28,832
between periods, primarily due to a decrease in rental income and an increase
in operating expenses.





                                      -11-
<PAGE>   13



                                   SIGNATURES



         Pursuant to the requirements of the Securities Exchange Act of 1934,
the registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto duly authorized.



                        NATIONAL HOUSING PARTNERSHIP REALTY FUND III
                        --------------------------------------------
                        (Registrant)
                        
                        
                        By:     The National Housing Partnership,
                                its sole General Partner
                        
                        
                        By:     National Corporation for Housing
                                Partnerships, its sole General Partner
                        
                        
                        
November 7, 1996        By:                        /s/
----------------                ----------------------------------------------
                                Jeffrey J. Ochs
                                As Vice President and Chief Accounting Officer





                                     -12-