Mayor Giuliani said last night that America must retain a military option for dealing with Iran’s nuclear program.

During a nationally televised appearance on Fox News’s “The O’Reilly Factor,” Mr. Giuliani, who is considering a run for the White House in 2008, said it would be “extremely dangerous” for Iran to have nuclear capability.

“I don’t think you can take the military option off the table,” he said. “You don’t have to wave that flag, but you have to leave that there as a possibility.”

In a swipe at the Democratic Party, which often finds itself attempting to shore up its national security credentials, the former mayor said having an American president that is viewed as “so much of an internationalist they’ll never exercise that option” would not be good for the country.

Mr. Giuliani, who has become a household name since leading the city after the attacks of September 11, 2001, also said that Israel should be given time to “destroy Hezbollah as much as possible.”

When the program’s notoriously aggressively host, Bill O’Reilly, asked why so many Americans oppose the Iraq war, Mr. Giuliani defended it and said having Sunnis, Shiites, and Kurds putting a government together is an accomplishment.

Mr. O’Reilly said he agreed with Mr. Giuliani on Israel and Iran, but seemed to bait him to the right when the conversation turned to immigration.

Mr. O’Reilly pointed out that illegal immigration had drastically increased under Mr. Giuliani’s tenure as mayor. Mr. Giuliani responded that the federal government was deporting only 1,500 undocumented immigrants a year while the city had roughly 400,000.

It is, however, social issues like immigration that could make running for the Republican presidential nomination difficult for Mr. Giuliani.

Political analysts say his liberal views on abortion, gun control, and gay rights will be hard to sell to the more conservative factions of the party.

Still, Mr. Giuliani has been steadily raising his profile and generating goodwill with Republicans nationwide. He has made appearances at GOP fundraisers and donated money to candidates from his political action committee, Solutions America, which has raised about $1.9 million.

Later this month, he is scheduled to travel to South Carolina for two GOP fund-raisers. The trip could be key, because the state is considered crucial in deciding the GOP presidential nominee.

The most recent Gallup Poll found that Mr. Giuliani was leading the pack of Republicans mentioned as possible presidential candidates. Roughly 29% of those surveyed said they favored the former mayor, while 24% supported Senator McCain, his nearest rival.

A professor of political science at the University of Virginia, Larry Sabato, said that despite the current poll numbers, Mr. Giuliani is vulnerable because Republicans who vote in the Iowa caucus and the South Carolina primary “have no clue that he is totally pro-choice and totally pro-gay rights.”

“It’s a long way from being talked about as a presidential candidate and running successfully for president,” he said.