Mayor Bloomberg’s dance around the city’s term limits law shows no signs of ending, as he said yesterday that the question of allowing a third term is one that is worthy of debate.

While Mr. Bloomberg said he agreed with term limits in general and that he is not trying to overturn them, he offered no clear support for the current two-term length.

“I think you can debate how many years it should be,” Mr. Bloomberg said at a press conference in Manhattan. He repeated the opinion a second time at the event, saying that while he believed term limits are democratic, “whether they should have been put in at two terms or three terms, that’s something you could debate.”

The mayor neither confirmed nor denied published reports that he had discussed the possibility of extending term limits with the editors of several New York newspapers, but said editorials would not sway the public’s views on the issues.

“I don’t know how influential any one group is in changing the public’s mind,” Mr. Bloomberg said. “I think the public is pretty smart: They get their information not from any one story or any one editorial, they get it over a long period of time.”

According to published reports, Mr. Bloomberg has discussed the possibility of legislating a third term with the City Council’s speaker, Christine Quinn, who is serving her second term and is considered a likely mayoral candidate in 2009. Ms. Quinn, through a spokeswoman, has denied such talks.

In addition to allowing Mr. Bloomberg to seek another term, such a move would give 35 City Council members who would be forced out by term limits in 2009 the opportunity to seek re-election. That could affect dozens of other races, as many term-limited members plan to run for other public positions. Mr. Bloomberg is scheduled to campaign today for one such council member, Simcha Felder of Brooklyn, who is challenging state Senator Kevin Parker of Brooklyn for his seat. The mayor and Mr. Felder are expected to appear together at a breakfast at the Midwood Senior Center in Brooklyn.