On his first trip to Iowa since decade-old sexual harassment allegations surfaced, Cain indirectly addressed the foreign policy problem by telling more than 200 people at a northeastern Iowa restaurant that the US needed to leave no doubt about its allies and enemies.

“My overriding philosophy relative to national security and foreign policy is an extension of the Reagan philosophy. Peace through strength,” Cain said, surrounded by Republican activists and employees from nearby offices. “We need to clarify our relationship with friends and enemies around the world and make sure we stand with our friends.”

Cain is a political novice who rose unexpectedly to become the top contender to challenge Mitt Romney, the favorite of the Republican establishment, but he looks to be fading under the weight of the sexual harassment allegations dating back to when he was president of the National Restaurant Association in the 1990s.

Those troubles have been compounded by what appears to be a thin knowledge of US foreign policy, though a top aide said after the Libya interview that Cain had not had enough sleep. Some polls show Cain drifting downward, ceding his place to former House of Representatives Speaker Newt Gingrich.

Cain commented a day after he hesitated during an interview with the Milwaukee Journal Sentinel editorial board, first saying he disagreed with President Barack Obama’s decision to back Libyan rebels, then adding that he likely would have done the same.

Cain seemed to contradict himself at Saturday’s Republican debate on whether waterboarding is acceptable when interrogating terrorism suspects. The Obama administration has banned waterboarding, which simulates drowning.

He has had other apparent missteps as well:

— On Oct. 18, he first said he could “see (himself) authorizing” the freeing of all detainees at Guantanamo Bay in exchange for a single detained US soldier. At a debate that night he said he did not recall making the comments, then that he misspoke.

— He has also said that “one very well-known Muslim voice” told him “that a majority of Muslims share the extremist views,” and has gone back and forth on whether he would authorize a war with Iran to stop its alleged nuclear program.

— On Oct. 31, he said that China, which has had nuclear weapons since the 1960s, was trying to “develop nuclear capability.” He has also gone back and forth over whether he wanted a large electric fence to deter immigrants from crossing from Mexico.

— He has also given confusing answers about his position on abortion.

On the Libya question, Cain said he paused while answering the question so he could collect his thoughts. He told his interviewers in Milwaukee that he had “all this stuff twirling around in my head.”

An aide later blamed Cain’s performance on lack of sleep.

In Iowa, Cain did not directly mention Libya during his 30-minute appearance, his second visit to the leadoff caucus state in the past three months. He spoke briefly to the crowd, shook hands, posed for pictures and toured the restaurant.

He took no questions from the audience or national and state reporters although Cain’s aides had promised an opportunity to question him.

Cain’s stop also came on the heels of a rocky stretch that began with questions about his loyalty to opposing abortion rights — a problem for influential evangelicals in Iowa.

But that issue was quickly eclipsed by the harassment allegations involving former subordinates when he headed the National Restaurant Association in the 1990s.

Four women say Cain harassed them. He denies the allegations.

Jim Budde, a Republican from nearby Bellevue, said he was leaning toward supporting Cain, but thought Cain took too long to address the harassment charges.

“Politics is a cutthroat business and you’ve got to address it head-on, and I think he was late on the draw,” Budde said. “I think it still hangs over his head.”

Cain remains a front-runner in Iowa, which holds its caucuses on Jan. 3, despite his stumbles and sparse campaigning there.

A new Bloomberg News poll of Iowa Republicans showed him clinging to a narrow lead in the state, with Texas Rep. Ron Paul, former Massachusetts Gov. Mitt Romney and former House Speaker Newt Gingrich closely bunched at the top.

Romney was in the important primary state of South Carolina on Tuesday, criticizing President Barack Obama for saying the US had grown “a little bit lazy” in trying to attract business investment.

The Republican former Massachusetts governor spoke from the floor of a Columbia sign-making factory during a brief stop in this first-in-the-South primary state.

“First, sometimes I just don’t think that President Obama understands America,” Romney said. “Now, I say that because this week, or was it last week, he said that Americans are lazy. I don’t think that describes Americans.”

Obama’s campaign spokesman said Romney’s got it wrong and that the president was trying to encourage business leaders to create jobs.