With skirmishes over immigration and security, Mayor Giuliani and Mitt Romney are taking aim at each other as they wait to see if their newly declared Republican rival, Fred Thompson, joins them at the top of the party’s presidential field.

In a GOP debate last night overshadowed by Mr. Thompson’s absence, Mr. Romney attacked Mr. Giuliani’s record on immigration as mayor, accusing him of opening the city’s doors to illegal immigrants and contributing to a four-fold increase in the number of undocumented immigrants nationwide.

Defending his policy of allowing illegal immigrants to report crimes and seek medical care without fear of deportation, Mr. Giuliani countered that he didn’t have “the luxury of political rhetoric” at a time when New York was the crime capital of America. “I had the safety and security of the people of New York City on my shoulders,” Mr. Giuliani said near the outset of the 90-minute debate, held at the University of New Hampshire.

Mr. Romney, a former Massachusetts governor, said Mr. Giuliani’s policy in New York amounted to “amnesty,” and he repeated his call to strip federal funding from so-called sanctuary cities.

The former mayor tried to return the fire later in the debate, using a question about gun control to note, with a glance at Mr. Romney standing next to him, that there was a 59% greater chance of being the victim of a crime in Boston than in New York.

The increasing tension between Messrs. Giuliani and Romney underscores their positions at the head of the GOP pack; Mr. Giuliani is leading in national polls, while Mr. Romney has a sizable lead in the earliest voting states, Iowa and New Hampshire.

That may all change with the entry of Mr. Thompson, the former Tennessee senator and “Law & Order” star who initiated a carefully choreographed debut by announcing his candidacy last night on NBC’s “The Tonight Show.”

He also bought a 30-second ad on Fox News — which broadcast the Republican debate — directing viewers to his campaign Web site, where a 15-minute video of him outlining the rationale for his candidacy was posted at midnight. He is now embarking on a five-day announcement tour through the early primary states, beginning today with stops in Iowa.

He comes into the race running second or third in many polls, and leading some state surveys, but questions linger about whether he has waited too long to get into the race.

Mr. Thompson’s absence from the stage loomed over the debate, and Fox News’s moderator, Brit Hume, made him the subject of the night’s first question, allowing nearly all the candidates an opportunity to crack a joke at his expense.

“Maybe we’re up past his bedtime,” Senator McCain of Arizona quipped, a veiled dig at murmurs that Mr. Thompson lacks the “fire in the belly” for a full-throttle presidential campaign.

Mr. Giuliani, a former federal prosecutor, joked that Mr. Thompson had “done a pretty good job of playing my part on ‘Law & Order.'” Mr. Giuliani’s campaign had another laugh at Mr. Thompson’s previous career earlier in the night, announcing the endorsements of actors Robert Duvall and Ron Silver shortly before the debate.

As with the four previous GOP debates, the discussion turned repeatedly to Iraq, including an unusual extended and emotionally charged exchange between a former Arkansas governor, Michael Huckabee, and an anti-war congressman of Texas, Rep. Ron Paul.

Shortly after Mr. Paul urged a quick and unconditional exit from Iraq, criticizing the 2002 invasion and repeating his claim that America’s presence in the Middle East had caused the September 11, 2001, attacks, Mr. Huckabee challenged him, saying that the initial decision to go to war was a “discussion the historians can have, but we’re there.”

“We bought it because we broke it,” Mr. Huckabee said. “We’ve got a responsibility to the honor of this country and to the honor of every man and woman who has served in Iraq and ever served in our military to not leave them with anything less than the honor that they deserve.”

Each response brought dueling eruptions of cheers from the audience, with Mr. Paul firing back that the “American people didn’t go in” to Iraq, and shouldn’t be punished by a continuation of the war. After Mr. Paul warned that the Republican Party would lose next year’s election because of American foreign policy, Mr. Huckabee retorted: “Even if we lose elections, we should not lose our honor, because that is more important than the Republican Party.”

The debate also featured awkward moments for several candidates, as Fox News cut away to questions from viewers watching the telecast at a New Hampshire diner. Confronted with disdain by the father of an American soldier in Iraq, Mr. Romney was forced once again to back away from comparing the work of his five sons for his presidential campaign to serving in the military. “There is no comparison, of course,” he said.

The twice-divorced Mr. Giuliani faced a question from a young man skeptical of voting for him because of his family life. “I’m not running as the perfect candidate for president of the United States. I’m running as a human being,” he said. Citing his record over 35 years, he said: “Obviously, any issues in my private life do not affect my public performance.”