Republican White House hopefuls set their sights high Thursday with some vowing they would shoot for the moon and restore American supremacy in space if elected.

"I do not want to be the country that having gotten to the moon first, turned around, said, it doesn't really matter, let the Chinese dominate space, what do we care?" former House speaker Newt Gingrich said.

"I think that is a path of national decline and I am for America being a great country, not a country in decline," he added to cheers at the final Republican debate before Florida's key presidential primary next week.

But his main rival, former Massachusetts governor Mitt Romney, shot down his proposals for a moon colony, accusing Gingrich of pandering to voters in Florida, where many jobs have been lost as the US space program has declined.

"That's an enormous expense and right now I want to be spending money here," Romney said. "I'm not looking for a colony on the moon. I think the cost of that would be in the hundreds of billions if not trillions. I would rather rebuild housing here in the US.

"I spent 25 years in business. If I had a business executive come to me, said they wanted to spend a few hundred billion dollars to put a colony on the moon, I'd say 'you're fired.'"

The issue is high on the agenda here after President Barack Obama, seeking re-election in the November elections, shuttered NASA's space shuttle program and is relying now on private firms to develop rockets to fly American astronauts back into space.

Gingrich argued that setting up a system of prizes and offering incentives would help private enterprise focus on developing spacecraft to propel Americans back into space.

"There are many things you can do to leverage accelerating the development of space. Lindbergh flew to Paris for a $25,000 prize," he argued, referring to Charles Lindbergh who was the first to complete a non-stop solo flight from the US to Paris in 1927.

But libertarian congressman Ron Paul hit back that he had no desire to send people back to the moon, even though as a young man he had dreamed of becoming the first doctor on the Earth's only satellite.

"I don't think we should go to the moon. I think we maybe should send some politicians up there sometimes," he quipped.

The fourth contender, former Pennsylvania senator Rick Santorum, agreed with Gingrich, saying: "I believe America's a frontier nation. And obviously the frontier that we're talking about is the next one, which is space."