WASHINGTON — For the second consecutive quarter, Mayor Giuliani has emerged as the front-runner in the Republican presidential fund-raising sweepstakes, garnering more than $11 million in this year’s third period, even as a Rasmussen poll appears to have dimmed his prospects.

The telephone survey found that 27% of Republicans would support a third party candidate backed by Christian conservative leaders if Mr. Giuliani, a supporter of abortion rights and gay rights, were to become the Republican nominee.

Mr. Giuliani led Senator McCain, who fired his campaign staff earlier this year after lower than expected fund-raising numbers and amassed $6 million in the most recent quarter. A former Massachusetts governor, Mitt Romney, was up $10 million for the quarter, but he loaned his campaign $8.5 million of his own money.

Mr. Giuliani’s campaign manager, Michael DuHaime, touted the campaign’s war chest, of which $10.5 million can be spent on the primary, as another example of the former mayor’s electability. “In a continued sign of growing support, our campaign has led the Republican field for the second quarter in a row in the fund-raising race,” Mr. DuHaime said. “We’re receiving real support from across the country because voters know Rudy Giuliani is the only candidate who has proven leadership, executive experience, and can beat the Democrats in November.”

“The mayor is the only candidate who has talked about the need for increasing of adoptions,” a spokeswoman for the Giuliani campaign, Maria Comella, said. “This is a solution-oriented goal that conservative Republicans can agree with.”

Nevertheless, the Rasmussen survey indicates that a Giuliani run in the general election could prompt social conservatives either to sit out the balloting or back a third party candidate. The chairman of Focus on the Family, James Dobson, has already said he would not vote for Mr. Giuliani under any circumstances, preferring to sit out the first presidential election of his adult life rather than cast a ballot for a man who favors legal abortion.

Mr. Romney could benefit from the social conservative backlash against Mr. Giuliani. Mr. Romney ran for office in Massachusetts as an abortion rights supporter, but he said he changed his views as governor after speaking with a Harvard University professor who was running an embryo farm.

A gay GOP organization, the Log Cabin Republicans, released an advertisement yesterday praising the former governor’s prior positions against social conservatives on gay issues, gun rights, and abortion. In the ad, a female narrator ends the spot saying, “A pro-choice record, Massachusetts values, Mitt Romney.”

Both Mr. McCain and a former senator of Tennessee, Fred Thompson, oppose legalized abortions. Currently, Mr. Thompson is second in national polls to Mr. Giuliani among likely Republican voters.

Among the second-tier Republican presidential candidates, Rep. Ron Paul of Texas, who has blamed the attacks of September 11, 2001, on American foreign policy and railed against what he calls a neoconservative conspiracy to launch the Iraq war, raised a little over $5 million.