New Yorkers say they like Mayor Bloomberg more than they like the idea of President Bloomberg.

The mayor’s job approval rating has risen to near an all-time high, 72%, but only two out of five city voters say they would likely cast their ballot for Mr. Bloomberg if he seeks the White House, a new Quinnipiac University poll has found.

“They don’t want him to go to the White House, but they like him down there at City Hall,” the director of Quinnipiac’s polling institute, Maurice Carroll, said.

Mr. Bloomberg has repeatedly shot down speculation that he may run for president in 2008, and most New Yorkers polled appeared to believe him — 62% said a Bloomberg bid was “not too likely” or “not likely at all.”

City voters are more supportive of Mr. Bloomberg’s heightened national profile. From gun control to immigration to stem cell research, the mayor has spoken out on a range of national issues in recent weeks, and 70% of registered New York voters said that this was good for the city.

“They see Bloomberg as their national leader,” a political consultant, Hank Sheinkopf, said. Mr. Sheinkopf said the 40% of New Yorkers who said they would probably or definitely vote for Mr. Bloomberg for president was “a pretty extraordinary number” for a man who has said he has no intention of running. That the number was not higher, he said, was a reflection of Mr. Bloomberg’s popularity as mayor.

The mayor’s 72% approval rating in the Quinnipiac poll was three points higher than in April and is approaching his high of 75%, recorded shortly after his re-election victory in November.

Voters in the Bronx appear to be the least worried about losing the mayor to Washington: Mr. Bloomberg’s job approval was lowest in that borough, at 55%, but his presidential support was highest, as 46% of respondents said they would probably or definitely vote for the mayor.

The mayor’s office had no comment on the poll.

Pollsters surveyed 1,041 registered city voters between July 5 and July 10. The margin of error was plus or minus three percentage points.

The poll also disclosed mixed feelings among New Yorkers about the redevelopment of ground zero. The number of voters who responded with a favorable impression of progress at the site dropped to 40% from 46% in April. More than half said they approved of new plans for the World Trade Center Memorial and the Freedom Tower.