An aggressive Mitt Romney repeatedly challenged Republican presidential rival Newt Gingrich in a fast-paced campaign debate Thursday night in Jacksonville, Fla., ridiculing the former House speaker's call to build costly projects in key primary states and to colonize the moon.

Romney vehemently denied Gingrich's own accusation that he is anti-immigrant — more so than any other candidate. And, as charges flew back and forth, Gingrich rebutted any suggestion that he couldn't rein in surging U.S. government spending.

"You don't just have to be cheap everywhere. You can actually have priorities to get things done," Gingrich declared, saying that as speaker of the House of Representatives he had helped balance the budget while doubling spending on the National Institutes of Health.

The debate was the second in four days in the run-up to next Tuesday's Florida primary. Opinion polls make the race a close one — slight advantage Romney — with two other contenders, former senator Rick Santorum of Pennsylvania and Texas Representative Ron Paul far behind.

Gingrich's upset victory in the South Carolina primary last week upended the race for the nomination to oppose Democratic President Barack Obama in the fall, and Romney in particular can ill afford a defeat on Tuesday.

While the clashes between Gingrich and Romney dominated the debate, Santorum drew applause from the audience when he called on the two front-runners to stop attacking one another and "focus on the issues."

"Can we set aside that Newt was a member of Congress … and that Mitt Romney is a wealthy guy?" he said in a tone of exasperation.

There were some moments of levity, including when Paul, 76, was asked whether he would be willing to release his medical records.

He said he was, then challenged the other three men on the debate stage to a 40-kilometre bike race. He got no takers.

The first clash occurred moments after the debate opened, when Gingrich responded to a question by saying Romney was the most anti-immigrant of all four contenders on stage. "That's simply inexcusable," the former Massachusetts governor responded.

"Mr. Speaker, I'm not anti-immigrant, my father was born in Mexico," Romney declared. "I'm not anti-immigrant."

At the same time, Romney noted that Gingrich's campaign had been pressured to stop running a radio ad that called Romney anti-immigrant after Florida Senator Marco Rubio called on Gingrich to do so.

He called on Gingrich to apologize for the commercial, but got no commitment.

About an hour later, Romney pounced when the topic turned to Gingrich's proposal for an permanent American colony on the moon — an issue of particular interest to engineers and others who live on Florida's famed Space Coast.

A career businessman before he became a politician, Romney said: "If I had a business executive come to me and say I want to spend a few hundred billion dollars to put a colony on the moon, I'd say, `You're fired."'

The audience erupted in cheers, but Romney wasn't finished.

He said the former speaker had called for construction of a new Interstate highway in South Carolina, a new Veterans Affairs hospital in northern New Hampshire and widening the port of Jacksonville to accommodate the larger ships that will soon be able to transit the Panama Canal.

"This idea of going state to state and promising people what they want to hear, promising hundreds of billions of dollars to make people happy, that's what got us into trouble in the first place," Romney said.

Gingrich responded that part of campaigning is becoming familiar with local issues.