# FORM 6-K
SECURITIES AND EXCHANGE COMMISSION Washington, D.C. 20549

# Report of Foreign Private Issuer

# Pursuant to Rule 13a-16
or 15d-16of the Securities Exchange Act of 1934

For the month
  of June, 2004Commission File Number 1-11080

THE ICA CORPORATION
HOLDING COMPANY(Translation of registrants name into English)

Minería No. #14511800 México D.F.
(Address of principal executive offices)

Form 20-F....X.....Form 40-F.........

Indicate by check mark if the
registrant is submitting the Form 6-K in paper as permitted by Regulation S-T Rule
101(b)(1): ____ 

Indicate by check mark if the registrant is submitting the Form 6-K in
paper as permitted by Regulation S-T Rule 101(b)(7): ____ 

Indicate by check mark whether by furnishing the information contained in this Form, the registrant is also thereby
furnishing the information to the Commission pursuant to Rule 12g3-2(b) under the
Securities Exchange Act of 1934.

Yes ..... No...X...

If Yes is marked, indicate
below the file number assigned to the registrant in connection with Rule 12g3-2(b): 82-
________

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| | PRESS
        RELEASE
| | ---------------------
|

|For more information
        contact:
      Ing. Alonso Quintana(5255) 5272-9991 x3468alonso.quintana@ica.com.mx
      Lic. Paloma
        Grediaga(5255) 5272-9991 x3470paloma.grediaga@ica.com.mx | in the United States:
        Zemi Communications
      Daniel Wilson
        (212) 689-9560d.b.m.wilson@zemi.com
|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | -----------------------------------------------------------------------------------------------------------------



ICA FLUOR SUBSIDIARY
SIGNS CONTRACTS TO BUILD FOUR OFFSHORE DRILLING PLATFORMS FOR PEMEX

Mexico City, June 21, 2004 ICA
Fluor, the industrial engineering company jointly owned by Empresas ICA Sociedad
Controladora (NYSE: ICA) and Fluor Corporation (NYSE: FLR), today announced that it has
signed four separate contracts, each for the fabrication of an offshore drilling platform
to be installed in the Gulf of Mexico, northeast region of the Campeche Bay.

The contracts, worth nearly $169
million dollars, were awarded by Pemex Exploración y Producción to a
subsidiary of ICA Fluor, Industria del Hierro (IH), located in Mata Redonda and Empalme,
Veracruz, Mexico.

The contracts are for the engineering,
procurement, construction, load out, sea-fastening and technical assistance during
installation of the platforms.

Total weight of the four platforms,
which are scheduled for completion in August 2005, is approximately 30,000 tons.

The four drilling platforms will help
to increase the oil production in the sea field of Ku-Maloob-Zaap, in the Gulf of Mexico,
to replace production from the Cantarell Field.

These four projects confirm the
ICA Fluor and Industria del Hierro positioning, competitiveness and success in the
offshore fabrication business, said Jorge Borja, ICA Fluors general director.

***Pemex Exploración y
Producción is a subsidiary of Pemex, the Mexican state-owned petroleum company.***

***ICA Fluor is the leading
  industrial engineering company in Mexico, dedicated to the engineering,procurement, and
  construction of telecommunication installations and chemical, petrochemical,automotive,

refinery and electricity generation plants.***

Industria del Hierro (IH) has
fabrication yards located in Mata Redonda and Empalme, Veracruz, and is 100% owned by ICA
Fluor. With more than 35 years of experience in the off-shore market, IH has executed more
than 60 marine projects; platforms from 30 to 70 meters of water, and processing of up to
40 thousand tons per year.

***Founded in 1947, ICA has
  completed construction and engineering projects in 21 countries. ICAs***
  ***principal business units include
  Civil Construction, and Industrial Construction. Through its
  
  subsidiaries, ICA also
  manages airports and operates tunnels, highways, and municipal services under government
  concession contracts and/or partial sale of long-term contract rights.***

***Fluor Corporation
  (NYSE:FLR) provides services on a global basis in the fields of engineering,***
  ***procurement, construction,
  operations, maintenance and project management. Headquartered in Aliso
  
  Viejo, Calif., Fluor is a
  FORTUNE 500 company with revenues of nearly $9 billion in 2003. For more
  
  information, visit
www.fluor.com.***

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|INVESTOR RELATIONS | www.ica.com.mx | 
|------------------ | -------------- | 



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SIGNATURE

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.

Date: June 21,
  2004

| | Empresas ICA Sociedad Controladora,
S.A. de C.V.                                  
| | ----------------------------------------------------------------------------------
| |                                                                                   
| | /s/ JOSE LUIS GUERRERO
Name: Dr. José Luis Guerrero
Title: Vice President, Finance