# 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 SIGNS PS. 196 MILLION CONTRACT TO UPGRADE THE TOLUCA INTERNATIONAL AIRPORT**

Mexico City, June 1, 2004
Empresas ICA Sociedad Controladora (NYSE and BMV: ICA), the largest engineering,
procurement, and construction company in Mexico, today announced the signing of a Ps. 196
million contract with Airports and Auxiliary Services for works on the Toluca
International Airport, in the State of Mexico.

The contract is a traditional,
unit-price public works contract, and includes the repaving of runway 15-33, taxiways,
platforms, widening of ramps in the hangar area, the construction of service roads, and
new visual landing aids. The airport will be the first in Mexico to use Category III-B
visual landing aids.

The project will have a term of 7
months, with work beginning on May 31 and scheduled completion on December 31, 2004. The
airport will continue in normal operation during the construction project.

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
develops housing, manages airports, and operates tunnels, highways, and municipal services
under government concession contracts and/or partial sale of long term contract rights.

#  #  #

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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 2,
  2004

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