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, 2004

Commission File Number 1-11080

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

Minería No. #145
11800 México D.F.
(Address of principal executive offices)

Indicate by check mark whether the registrant files or will file annual reports under cover Form 20-F or Form 40-F.

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- ________

PRESS RELEASE

For more information contact: Ing. Alonso Quintana
(5255) 5272-9991 x3468
alonso.quintana@ica.com.mx Lic. Paloma Grediaga
(5255) 5272-9991 x3470
paloma.grediaga@ica.com.mx in the United States:
Zemi Communications Daniel Wilson
(212) 689-9560
d.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.

INVESTOR RELATIONS www.ica.com.mx

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