For the month of June 2004

Commission File Number: 333-13580

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Mexico City, June 1, 2004-Telefonos de Mexico, S.A. de C.V. (TELMEX) (BMV: TELMEX; NYSE: TMX; NASDAQ: TFONY; LATIBEX: XTMXL) announced today that ADS holders of Chilesat Corp. S.A. will have until no later than 5:00 p.m., New York City time today, June 1, 2004, to tender their shares represented by ADSs.

Offer Details

On May 4, 2004, Telmex Chile launched its public tender offer to acquire up to 60% of the outstanding shares of Chilesat, a telecommunications company, at a price of $154.23 Chilean Pesos per share of common stock, in order to obtain control of the company. The offer will expire at 5:30 p.m., New York City time, on June 3, 2004 unless extended. The offer is being made to all shareholders of Chilesat. The offer is not being made for the American Depositary Shares (ADSs) of Chilesat and there will be no separate offer in the United States to acquire the ADSs. In order for holders of ADSs to participate in the offer, they must tender the shares represented by their ADSs to The Bank of New York, the U.S. tender agent of the offer no later than 5:00 p.m., New York City time, on June 1, 2004 unless extended.

Where you can find additional information:

We urge investors and security holders of Chilesat to read carefully the amended and restated prospectus regarding the proposed transaction because it will contain important information about the transaction. Investors and security holders will be able to obtain a free copy of the amended and restated prospectus and other documents filed by Telmex with the U.S. Securities and Exchange Commission (SEC) at its website at www.sec.gov. These documents may also be obtained from Banchile Corredores de Bolsa S.A. by calling 800 202820 and from Georgeson Shareholder Communications Inc., the Information Agent, by calling 1-800-335-9439.

About TELMEX

Telmex is the leading telecommunications company in Mexico with 16.1 million telephone lines in service, 2.5 million line equivalents for data transmission and 1.5 million internet accounts. Telmex offers telecommunications services through an almost 75 thousand kilometer fiber optic digital network. Telmex and its subsidiaries offer a wide range of advanced telecommunications, data and video services, internet access as well as integrated telecom solutions for corporate customers. Additionally, the company offers telecommunications services through its affiliates in Argentina, Brazil, Colombia, Chile and Peru. More information about Telmex can be accessed on the internet at www.telmex.com.

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This press release is for information purposes only. The solicitation of offers to buy shares will only be made pursuant to the prospectus and related materials that Telmex will file and make available to shareholders of Chilesat. This communication shall not constitute a solicitation of an offer to purchase in any state in which such offer, solicitation or sale would be unlawful.

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This press release contains forward looking statements concerning the financial condition, results of operations and business of Telmex following the consummation of their proposed acquisition of Chilesat and the anticipated financial and other benefits of such proposed acquisition. In some cases, you can identify forward looking statements by the words "will", "believes", "plans", "would" or similar expressions. These forward looking statements are not guarantees of future performance and are subject to risks and uncertainties and other important factors, including those that could cause actual results to differ materially from expectations based on forward looking statements made in this press release or elsewhere. For a description of certain of these risks please refer to Telmex's filings with the SEC.