While Mayor Bloomberg dodged a question about whether there was anything that would change his mind about running for president, a Rupert Murdoch-financed poll showing there is nationwide support for the idea isn’t changing the mayor’s mind about a White House bid.

“I can’t tell you that I didn’t get a smile on my face when I saw it,” Mr. Bloomberg said when asked about the New York Post/Fox News Channel poll. The survey of 800 registered voters found that 81% would consider an independent presidential candidate in 2008 and 41% would consider Mr. Bloomberg if he ran.

The mayor, a registered Republican and former Democrat, has sought out a national profile on several key issues early in his second term, fueling speculation that his eye is on the White House. He has repeatedly denied the ambition, and did so again yesterday, saying, “I am not running for president, for the record.” He joked that it would be “a tough commute from 79th Street,” where he lives in a town house.

He did suggest that the country was ready for a candidate outside the two-party system.

“I think that the public in this country wants government to function better than it has been functioning,” the mayor said. “You don’t need this poll to tell you that. You only need to go and see how many people register to vote across this country and don’t select a party.”

“I think these are people who clearly care,” he said, “because they are going to the effort to register, but they aren’t happy with partisan politics.”

In his first term, Mr. Bloomberg failed in an effort to make city elections nonpartisan. He said yesterday he thought state and national elections should be nonpartisan.