Mayor Rudolph Giuliani, who has won widespread praise for his stewardship of the city since the terrorist attacks, did not rule out trying to extend his stay in office but said Monday he hasn't had time to decide.

"I have not had time to think about it," said the mayor, who is barred by term limits from seeking a third term this fall. "It's a very important decision. I need time to talk to people about it."

The mayoral primary is Tuesday. The Republican mayor had previously said he did not wish to discuss politics as he concentrated on recovery from the Sept. 11 attack on the World Trade Center.

But a source close to the mayor told The Associated Press on condition of anonymity that Giuliani has talked with advisers about extending his stay in office past Dec. 31, when his term expires.

It was unclear whether the mayor would try to have the law amended so voters could vote for him or whether he would try to extend his current term.

Giuliani refused to comment on the speculation, instead urging voters to turn out for Tuesday's Democratic and Republican mayoral primaries and select from among the candidates on the ballot.

"I need time to reflect on what I am going to do and it would not involve the primary anyway," Giuliani said. "It would not make sense to write my name in."

The general election is Nov. 6.

For Giuliani to be eligible to continue serving beyond a second term, the Legislature and Republican Gov. George Pataki would have to enact emergency legislation to extend his term, or the City Council and city voters would have to amend the City Charter.

Neither scenario is likely because mayoral candidate and City Council Speaker Peter Vallone -- as well as top legislative leaders -- have said they do not want to override city voters, who enacted the term limits law in 1993 and again in 1996.

A bid to repeal term limits failed in the City Council at the committee level in March. Giuliani also was a strong supporter of term limits when they were first considered in the early 1990s.

Vallone, Public Advocate Mark Green, Bronx Borough President Fernando Ferrer and Comptroller Alan Hevesi also are seeking the Democratic nomination in Tuesday's primary. Media owner Michael Bloomberg and former congressman Herman Badillo are seeking the Republican nomination.

Giuliani's popularity has skyrocketed since two hijacked jets brought down the Trade Center.

After barely escaping with his life from a building adjacent to the twin towers, the mayor calmly informed his fellow New Yorkers that the death toll would be "more than any of us could bear." More than 6,400 are missing and feared dead.

The mayor has worked around the clock, holding news conferences in between visits to the disaster site, funerals and meetings to coordinate the response. He has won bipartisan praise and has been cheered across New York.

Over eight years, the mayor steered the city into an era of lower crime and prosperity, but his often combative style irritated and alienated many New Yorkers. Allegations of police misconduct and fatal shootings by police officers angered the city's minority community.

The mayor ran for Senate from New York last year against Hillary Rodham Clinton but dropped out of the race six months before the election amid revelations that he had prostate cancer and a girlfriend. His often-nasty divorce was headline news.

A poll conducted Sept. 18-19 by the Marist College Institute for Public Opinion indicated that registered city voters were divided over whether to postpone the election because of the disaster.

Asked if they would favor a one-year postponement, 49 percent said no and 45 percent said yes, within the poll's 5 percentage-point margin of error. The same poll showed voters were against rescinding term limits for citywide officeholders, 57 percent to 33 percent.