Mayor Bloomberg’s newly ambiguous position on term limits is drawing the ire of one of his potential successors, Comptroller William Thompson Jr., who is demanding that Mr. Bloomberg make his intentions on the issue known.

“If the mayor’s position has changed on term limits, then I think he needs to be honest and direct with the voters,” Mr. Thompson, a candidate for mayor in 2009, said yesterday in an interview. “I think the public is owed an explanation now — and quickly.”

Mr. Thompson described as a “charade” Mr. Bloomberg’s recent softening of his stance on term limits, and said that any proposed changes to term limit laws should be put to a voter referendum and not decided by the City Council.

Mr. Bloomberg has said that he would consider signing legislation extending term limits if the City Council passed such a bill. According to Mr. Thompson, such a legislative effort “would undermine everything” Mr. Bloomberg has said on the issue. Mr. Bloomberg has said that he supports the current term limit laws, which were approved by referendums in 1993 and 1996, and would like to see the City Council stripped of its ability to override them.

Mr. Thompson declined to say whether he would continue to run for mayor or run for re-election as comptroller were the law changed.

The council’s speaker, Christine Quinn, said yesterday that she has held no discussions with the mayor or any of his senior staff regarding term limits.

“In my opinion, this is all just much ado about nothing,” Ms. Quinn said.

Asked about Mr. Thompson’s comments, Mr. Bloomberg declined to offer his opinion at a press conference in Brooklyn yesterday.

“I think it is absolutely a great example of what America is all about. The comptroller has the right to state his opinion any time he wants,” Mr. Bloomberg said.