Under pressure from Vodafone, Cingular Wireless increased its own offer to about $35 billion (£18.6 billion) in cash shortly before the auction deadline on Friday evening.

The high price fetched by AT&TW will increase concerns among Vodafone’s shareholders, many of whom are sceptical about the financial merits of the deal. Some analysts have estimated that buying AT&TW could dilute Vodafone’s earnings by more than 20%.

Merrill Lynch, the bank advising AT&TW, was this weekend urging the bidders to clarify and improve their offers.

Vodafone may have to offer substantially more than Cingular to win a recommendation from the AT&TW board. It would first have to sell its 44.3% stake in Verizon Wireless, America’s leading mobile network operator.

Although Verizon Communications, the owner of the controlling stake, is keen to take full control of its mobile arm, the deal would be subject to regulatory scrutiny — posing the threat of months of delay.

As a foreign buyer, Vodafone may face particular difficulties. Singapore Technologies Telemedia’s refinancing of the insolvent Global Crossing, the international fixed-line telecoms group, was delayed for months because of such concerns.

Details of Vodafone’s tactics in the auction remain shrouded in secrecy. Late on Friday, bankers working for Cingular were still seeking confirmation that the British company had submitted a bid. Some British shareholders even hoped that Vodafone was playing an elaborate game of poker, with the aim of forcing Cingular to pay more than it otherwise would.

Nextel, another, smaller, American mobile group, is believed not to have made an offer. NTT DoCoMo, the Japanese company that is the largest shareholder in AT&TW, has also decided not to bid. Shareholders are concerned that Vodafone is swapping $1 billion of annual dividends from Verizon Wireless for control of a company that has an ageing network and is rapidly losing customers to rivals.

The purchase of AT&TW would allow Vodafone to use its brand in America’s large and still-growing market, and take the group into the Caribbean.

But some American experts believe that AT&TW has deep-seated problems that Vodafone will struggle to fix.

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