ALBANY – Mayor Giuliani would beat New York’s attorney general, Eliot Spitzer, in a hypothetical race for governor despite Mr. Spitzer’s commanding lead over a number of other high-profile Republicans regarded as potential opponents next year, according to a new independent poll.

According to a Quinnipiac University poll released yesterday, Mr. Giuliani beat Mr. Spitzer by 49% to 42% in a head-to-head matchup. The poll showed Mr. Spitzer beating the district attorney of Westchester, Jeanine Pirro, by 59% to 21% in the same race. Mr. Spitzer, who is regarded as the presumptive Democratic nominee, would bury the former governor of Massachusetts, William Weld, 60% to 16%.

Mr. Giuliani’s lead over Mr. Spitzer in the poll suggests that a Republican could stand a chance against the popular attorney general, who had been leading Governor Pataki in polls for months before the governor’s announcement last week that he will not seek re-election next year to a record fourth, four-year term.

Looked at another way, however, Mr. Giuliani’s lead shows just how daunting next year’s gubernatorial race will be for Republicans, since the former two-term mayor has shown no interest in running against Mr. Spitzer. A Giuliani spokeswoman yesterday for the first time flatly ruled out a run for governor or any other statewide race.

“Rudy Giuliani remains committed to sustaining the ongoing success of his consulting firm, Giuliani Partners, and has no intention of running in 2006,” the spokeswoman, Sunny Mindel, said yesterday. “Anything that’s coming up in 2006, he’s not running for.”

The governor’s race is not the only headache for Republicans going into 2006. Senator Clinton maintains a 66%-23% lead over Mrs. Pirro in a hypothetical matchup for U.S. Senate, according to the Quinnipiac poll. Mrs. Pirro has not yet said whether she will run for Senate, attorney general, or governor.

The director of the Quinnipiac poll, Maurice Carroll, ascribed Mr. Giuliani’s popularity to his performance four years ago in the aftermath of the terrorist attacks of September 11, 2001.

“He wins everything since 9/11,” Mr. Carroll said. “Giuliani is unbeatable in a poll since then.”

The poll, which was conducted in the days following Governor Pataki’s announcement that he will not seek another term, also showed Mrs. Clinton beating a Manhattan lawyer and former son-in-law of Richard Nixon, Edward Cox, by 64% to 26%. Mr. Carroll said Mrs. Clinton will be tough to beat, regardless of her opponent.

“She’s a very formidable candidate,” Mr. Carroll said. “A lot of people don’t like her, but a lot of people do.”

The Quinnipiac poll came from phone interviews with 1,498 registered voters statewide conducted in the five days ending Monday. The sampling error is said to be 2.5 percentage points.