In a statement, Vodafone said it concluded that it was ``no longer in its shareholders' best interests to continue discussions.''
Vodafone's announcement came after The Wall Street Journal reported on its Web site early Tuesday, citing people familiar with the matter, that Cingular Wireless won the bidding war with Vodafone with an offer of $15 a share, or about $40.5 billion.
David Caouette, a spokesman for Redmond, Wash.-based AT&T Wireless, told The Associated Press early Tuesday the company had no comment. Several messages left by the AP for Cingular spokespeople were not immediately returned.
In Tuesday's statement, the British company said it remained "committed to its existing position in the U.S. market with its successful partnership in Verizon Wireless."
Earlier this month, Vodafone said it was considering bidding for AT&T Wireless. The company on Monday matched Cingular Wireless' $38 billion bid for AT&T Wireless, a source told The Associated Press on condition of anonymity.
Vodafone had no comment on details of its bid.
Cingular, the United States' No. 2 mobile phone provider with 23.4 million customers, early Monday offered $14 a share for AT&T Wireless, after offering $13 a share, or $35 billion, over the weekend, two sources said.
A Vodafone deal would have required the British cell-phone giant to sell its 45 percent stake in Verizon Wireless, the biggest mobile phone company in the United States.
In Paris, shares in Vivendi Universal SA rose 4.5 percent in early trading on speculation that Vodafone would now turn its attention to the French company, hoping to gain control of SFR-Cegetel. The telecoms unit account for almost a third of Vivendi's revenue.
AT&T Wireless' share price has risen steadily in recent weeks on news that it was putting itself on the auction block. The carrier has more than 22 million subscribers, including a sizable base of corporate clients who tend to use more services and spend more money.
But the company has struggled in recent months.
Late last year, it couldn't add new subscribers because of a glitch in a new software system. The company also has acknowledged that it has lost more customers than it had gained under the new federal rules that took effect in late November allowing cell phone users to change carriers without losing their phone numbers. The company has not released specific figures.