When New York City voters are asked whom they’d like as their next mayor, Mayor Bloomberg is the top pick. The problem is, the mayor is term-limited and a majority of voters, 56%, say they are opposed to extending the city’s term limits to allow him to run for re-election, according to a new poll.

When New Yorkers are given the names of seven potential next mayors, Mr. Bloomberg wins support from 38% of voters. Commissioner Raymond Kelly is the second-most popular pick for mayor, followed by the president of Brooklyn, Marty Markowitz, the Quinnipiac University poll released yesterday found.

Rep. Anthony Weiner, who is running for mayor, won the support of 10% of voters surveyed, and Comptroller William Thompson Jr. and Speaker Christine Quinn each won support of 7% of city voters. Public Advocate Betsy Gotbaum secured 4%.

Mr. Kelly has said he is not running for mayor, while Mr. Markowitz has said he has not yet made up his mind about whether to run.

When asked about term limits, 55% of voters said it would be unfair to change the rules in “the middle of the game,” while 40% said Mr. Bloomberg should have another term to complete his work as mayor.

The poll found that 54% of New Yorkers say the mayor’s takeover of the city’s schools has been a success, but 29% said the next mayor should keep total control of the schools, with 55% favoring a system where the mayor shares control of the schools with an independent school board.

New Yorkers are opposed to a congestion pricing plan, with 58% of voters saying they do not want to try again to implement it.

Mr. Bloomberg’s approval rating is 71%. The same percentage of New Yorkers said they support the basic concept of term limits.

Quinnipiac University surveyed 999 registered voters in the city between July 10 and July 14. The poll has a margin of error of plus or minus 3.1 percentage points.