Mike Huckabee on Tuesday called for a halt on visas for immigrants who come from countries that sponsor or harbor terrorists, potentially energizing the debate over immigration as Republican candidates head to South Carolina for the Jan. 19 primary.

"These are folks who have overstayed their welcome. Every one of the 19 hijackers on 9/11 came here legally. Our government welcomed them in," Huckabee said in Rock Hill, S.C., shortly after flying from Michigan, which held its primary Tuesday.

"Well there's a couple of things that we're going to do differently. I say we ought to put a hiatus on people who come here... if they come from countries that sponsor and harbor terrorists. Let's say until you get your act in order and we get our act in order we're not going to just let you keep coming and threaten the future and safety of America," Huckabee said.

Huckabee didn't mention the proposal at his second stop, a rally of about 250 in Sumter. Afterward, his new senior adviser, Jim Pinkerton, backed away from the proposal, saying that Huckabee really meant that wants a "thorough review" of immigration policies.

"It was crazy that of the 9/11 hijackers, they had 63 pieces of fake identification between them, and we're not going to let that happen," Pinkerton said. "Whatever it takes to cease and desist that, he'll do it.

The national commission that studied the Sept. 11, 2001, attacks concluded that at least two of the 19 terrorists and possibly 11 others presented fraudulently altered passports when they entered the United States.

The State Department identifies five countries as state sponsors of terrorism: Cuba, Iran, North Korea, Sudan and Syria.

The former Arkansas governor has been criticized by his rivals for supporting tuition breaks for the children of illegal immigrants in Arkansas.

But Huckabee began to tighten his policies in early December when he released a nine-point immigration plan. The plan called for a border fence and a zero-tolerance policy toward amnesty, and stated that all illegal immigrants would have a 120-day window to register and leave the country.

FOX News' Serafin Gomez and The Associated Press contributed to this report.