Exhibit (a)(5)(i)

Qwest Communications International Inc. Announces Cash Tender Offer for 3.50%

Convertible Senior Notes Due 2025

DENVER, July 13, 2010 – Qwest Communications International Inc. (NYSE:Q) today announced a tender offer to purchase for cash any and all of its $1.265 billion outstanding 3.50 percent convertible senior notes due 2025 (“Convertible Notes”).

Upon the terms and subject to the conditions set forth in the company’s Offer to Purchase, dated July 13, 2010 (the “Offer to Purchase”), and the related Letter of Transmittal, the company is offering to pay, in cash, for each $1,000.00 principal amount of Convertible Notes validly tendered (and not validly withdrawn) pursuant to the offer, consideration equal to the sum of:

• the Average VWAP (as defined below) of the company’s stock multiplied by 206.3354 (which is the number of shares of the company’s common stock currently issuable upon conversion of $1,000 principal amount of Convertible Notes); plus

• a fixed cash amount of $30.00

In no event will the consideration for the purchase price be less than $1,000.00 or more than $1,170.00 per $1,000.00 principal amount of such Convertible Notes.

“Average VWAP” is the arithmetic average of the “Daily VWAP” of the company’s stock on each trading day during the period of 20 consecutive trading days beginning on Wednesday, July 14, 2010, and ending on Tuesday, Aug. 10, 2010. The Daily VWAP represents the per share volume-weighted average price of the company’s common stock for a given day as shown on the Bloomberg Q.N<EQUITY>AQR page (or its equivalent successor if such page is not available).

Prior to determining the final purchase price, an indicative purchase price will be posted on the website www.gbsc-usa.com/Qwest and will be available from the Information Agent for the offer. The company will determine the final purchase price promptly after the close of trading on the New York Stock Exchange on Aug. 10, 2010. The final purchase price also will be posted on the above-mentioned website and available from the Information Agent.

Accrued interest to, but excluding the settlement date, also will be paid in cash on all Convertible Notes purchased in the offer.

The offer is scheduled to expire at 5 p.m. EDT on Thursday, Aug. 12, 2010 (the “Expiration Date”), unless extended or earlier terminated. The offer is subject to the satisfaction or waiver of certain conditions. The offer is not subject to the receipt of any minimum amount of tenders.

Upon the terms and subject to the conditions set forth in the Offer to Purchase and related Letter of Transmittal, holders who validly tender (and do not validly withdraw) their notes at or prior to 5 p.m. EDT on the Expiration Date, and whose notes are accepted for purchase, will receive payment of the purchase price on the settlement date, which is expected to be Aug. 13, 2010.

The complete terms and conditions of the offer are set forth in the Offer to Purchase and related Letter of Transmittal that are being sent to holders of notes. Copies of the Offer to Purchase and Letter of Transmittal may be obtained from the Information Agent for the offer, Global Bondholder Services Corporation, at (866) 540-1500 (US toll-free) or (212) 430-3774 (collect).

Goldman, Sachs & Co. is acting as the Dealer Manager for the tender offer. Questions regarding the offer may be directed to Goldman, Sachs & Co. at (800) 828-3182 (US toll-free) and (212) 902-5128 (collect).

As previously announced, the company has entered into a merger agreement with CenturyLink, Inc. (the “Merger Agreement”). The Merger Agreement requires that Centurylink and the company coordinate with each other to designate the record dates and payment dates for CenturyLink’s and the company’s respective quarterly dividends. Thus, the timing of the company’s future dividends may deviate from historical dates due to this requirement. In addition, the Merger Agreement limits the company’s ability to pay quarterly dividends that exceed $0.08 per share.

This press release does not constitute an offer to purchase, or the solicitation of an offer to sell, securities. The tender offer will be made solely by the Offer to Purchase dated July 13, 2010, and the related Letter of Transmittal. An issuer tender offer statement on Schedule TO, including the Offer to Purchase and the related Letter of Transmittal, describing the offer will be filed with the Securities and Exchange Commission. Holders are encouraged to read the Schedule TO and its exhibits carefully before making any decision with respect to the offer because it contains important information. The Schedule TO, the Offer to Purchase, the Letter of Transmittal and other related offer materials will be available free of charge at the website of the Securities and Exchange Commission at www.sec.gov or from the Information Agent as described above.

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Forward-Looking Statement Note

This release may contain projections and other forward-looking statements that involve risks and uncertainties. These statements may differ materially from actual future events or results. Readers are referred to the documents filed by us with the Securities and Exchange Commission, specifically the most recent reports which identify important risk factors that could cause actual results to differ from those contained in the forward-looking statements, including but not limited to: access line losses due to increased competition, including from technology substitution of our access lines with wireless and cable alternatives, among others; our substantial indebtedness, and our inability to complete any efforts to further de-lever our balance sheet; adverse results of increased review and scrutiny by media and others (including any internal analyses) of financial reporting issues and practices or otherwise; rapid and significant changes in technology and markets; any adverse developments in commercial disputes or legal proceedings; potential fluctuations in quarterly results; volatility of our stock price; intense competition in the markets in which we compete including the effects of consolidation in our industry; changes in demand for our products and services; acceleration of the deployment of advanced new services, such as broadband data, wireless and video services, which could require substantial expenditure of financial and other resources in excess of contemplated levels; higher than anticipated employee levels, capital expenditures and operating expenses; adverse changes in the regulatory or legislative environment affecting our business; changes in the outcome of future events from the assumed outcome included in our significant accounting policies; our ability to utilize net operating losses in projected amounts; and continued unfavorable general economic conditions. In addition, actual results could be affected by factors relating to our pending merger with CenturyLink, including but not limited to: the ability of the parties to timely and successfully receive the required approvals of regulatory agencies and our respective stockholders; the possibility that the anticipated benefits from the acquisition cannot be fully realized or may take longer to realize than expected; the possibility that costs or difficulties related to the integration of our operations into CenturyLink will be greater than expected; the ability of the combined company to retain and hire key personnel; and other risk factors and cautionary statements as detailed from time to time in each of CenturyLink’s and our reports filed with the Securities and Exchange Commission.

The information contained in this release is a statement of Qwest’s present intention, belief or expectation and is based upon, among other things, the existing regulatory environment, industry conditions, market conditions and prices, the economy in general and Qwest’s assumptions. Qwest may change its intention, belief or expectation, at any time and without notice, based upon any changes in such factors, in Qwest’s assumptions or otherwise. The cautionary statements contained or referred to in this release should be considered in connection with any subsequent written or oral forward-looking statements that Qwest or persons acting on its behalf may issue. This release may include analysts’ estimates and other information prepared by third parties for which Qwest assumes no responsibility.

Qwest undertakes no obligation to review or confirm analysts’ expectations or estimates or to release publicly any revisions to any forward-looking statements and other statements to reflect events or circumstances after the date hereof or to reflect the occurrence of unanticipated events.

By including any information in this release, Qwest does not necessarily acknowledge that disclosure of such information is required by applicable law or that the information is material.

The marks that comprise the Qwest logo are registered trademarks of Qwest Communications International Inc. in the U.S. and certain other countries.

Contact Information:

Media Contact

Diane Reberger

303-992-1662

Diane.Reberger@qwest.com

Investor Contact

Nhung Van

303-896-7844

nhung.van@qwest.com