While New Yorkers aren’t wildly excited about the idea of Mayor Bloomberg making a presidential run, he does get higher marks than his predecessor as a potential commander-in-chief in a new Quinnipiac University poll.

Forty-four percent of respondents said Mr. Bloomberg would make a “great” or “good”president, while 41% said the same about Mayor Giuliani. Neither of the Republicans came close to matching Senator Clinton, however. Two-thirds of New Yorkers said she would be a great or good president.

The poll also indicated that Governor Pataki shouldn’t bank on city support if he decides to seek the White House, as is widely expected. Just 19% of respondents in the five boroughs said he would be a success as president.

Despite skepticism about Mr. Bloomberg’s presidential prospects, his popularity at City Hall has not waned. His approval rating stands at 72%, where it has held for more than a year since he decisively won election to a second term.

Pollsters surveyed 1,314 registered city voters for five days ending on Sunday. The margin of error was plus or minus 2.7%.

The poll was taken before the disclosure on Monday that Mr. Giuliani has taken the first step toward a full-fledged bid for the presidency, forming an exploratory committee that will allow him to “test the waters” by raising money and building a campaign organization.

Support for Mrs. Clinton among city voters is not surprising, given New York’s history as a Democratic stronghold. She has deflected questions about a White House bid but would enter the race as a front-runner for her party’s nomination.

A spokesman for the mayor, Stuart Loeser, said Mr. Bloomberg is “gratified” by New Yorkers’ appreciation of his performance at City Hall. He did not address the question of a Bloomberg presidency, and the mayor has repeatedly said he has no intention to run for higher office. Less than 40% of respondents said they thought Mr. Bloomberg would run, and 35% said they would “probably” or “definitely” vote for him if he ran as an independent. One-third said it was likely he would win.

The Quinnipiac poll also found strong job approval for the City Council speaker, Christine Quinn, and the city comptroller, William Thompson Jr. — at least among New Yorkers who have an opinion about them. Forty-seven percent approved of Ms. Quinn’s performance in her first year in office, while 45% responded favorably to Mr. Thompson. Just 12% disapproved of their performance, with the rest undecided. There was somewhat less support for the public advocate, Betsy Gotbaum, who has drawn some criticism that she is not active enough in office.