WASHINGTON — Mayor Giuliani is cool to the idea of an immediate presidential pardon for I. Lewis Libby Jr., a position that puts him out of step with some conservatives who say President Bush should not wait to grant the convicted former White House aide a legal reprieve.

“The pardon power is a very, very important power that the president has, and it has to be exercised very judiciously and very carefully,” Mr. Giuliani told reporters in Washington yesterday. “You certainly shouldn’t speculate about it while a criminal case is still ongoing.”

He added: “It seems to me you let it go through the process.”

Mr. Giuliani is a former federal prosecutor who has a complicated relationship to the pardon process. He noted yesterday that he briefly ran the pardon office when he served in the Justice Department. “I know more about pardons than anybody needs to know about them,” he said.

But he has also been on the other side: Mr. Giuliani prosecuted the commodities broker Marc Rich for tax evasion when Mr. Giuliani was the U.S. attorney for New York’s Southern District. President Clinton pardoned Mr. Rich shortly before he left office in 2001, and Mr. Giuliani, then the mayor of New York, was so upset that he canceled a meeting with Senator Clinton weeks after she was sworn in.

Mr. Giuliani’s stance matches that of the White House, which has refrained from publicly discussing a pardon while Libby asks for a new trial and appeals his conviction. A federal jury last week found the former chief of staff to Vice President Cheney guilty of perjury and obstruction of justice, saying he lied under oath about his role in the leaked identity of a CIA agent in 2003.

Reaction to the conviction has fallen largely along party lines, with some conservative commentators and editorial writers calling for Mr. Bush to immediately pardon Libby rather than wait for an appeal and application process to run its course, as Mr. Giuliani suggested. They argue that Libby, who was never charged with the leak itself, was the victim of an overzealous special prosecutor, Patrick Fitzgerald.

Some Democrats, meanwhile, have urged the president to rule out a pardon and say the conviction is a validation of claims that the Bush administration misled the country in the run-up to the Iraq war.

Libby, who faces sentencing June 5, could remain free pending an appeal, which could drag well into next year.

A CNN poll released yesterday found that 69% of Americans oppose a pardon for Libby. Pollsters also asked respondents if they thought Mr. Cheney was “part of a cover-up to try to prevent the special prosecutor from getting to the truth” of who leaked the identity of the CIA agent, Valerie Plame, to the press. Fifty-two percent said yes.

Mr. Giuliani tried to steer clear of the partisan divide yesterday, focusing instead on the precedent of pardons, citing the rehabilitation of drug dealers as an example. “I believe in pardons, meaning I believe there are people who can redeem themselves and change their lives,” he said.

Running on his credentials on national security and cutting crime and taxes, Mr. Giuliani has led the early polling in the race for the Republican nomination, despite his differences with conservatives on several issues including abortion, gay rights, and gun control. A GOP strategist, Rich Galen, said that while a difference on the pardon issue may not change many minds, Mr. Giuliani may run the risk of reaching a tipping point where conservatives rethink their support for him. If that happens, “Conservatives will finally say, ‘He ain’t that good,'” Mr. Galen said.

Looking to convert the skeptics, Mr. Giuliani yesterday announced the support of a socially conservative lawmaker, Senator Vitter of Louisiana. “After numerous personal meetings with the mayor, it’s very clear to me that he’s not running for president to advance a liberal social agenda,” Mr. Vitter said.

Mr. Giuliani also took a step to the right on guns, saying yesterday that he agreed with a federal appeals court ruling striking down a District of Columbia ban on handguns in homes.