WASHINGTON - Mitt Romney looked to build on his growing strength in the scrambled Republican presidential race as the eight candidates vying for the chance to challenge President Barack Obama in 2012 prepared for a Saturday night debate focused on foreign policy.

U.S. relations with Israel and Iran, and China's trade and currency policies were subjects likely to arise, a twist in a campaign in which the Republicans have relentlessly attacked Obama on the weak U.S. economy and the loss of U.S. jobs.

Romney's strategy is to maintain the steady, it's-all-about-the-economy campaign that's landed him in the top tier and, behind the scenes, prepare for any of his rivals to rise in the race.

"I know there will be one or two others that will be doing well in the polls, that'll be you know, be real contenders. That's the nature of the process," the former Massachusetts governor told reporters after spending Friday campaigning at a barbecue restaurant near Greenville, South Carolina.

The difficulties of two of his main opponents have given a boost to Romney with less than two months to go before the Iowa caucuses, the first nominating contest.

Romney's closest rival, businessman Herman Cain, was in New York doing interviews defending himself against allegations he sexually harassed four women in the 1990s.

And Texas Gov. Rick Perry was spending nearly $1 million airing ads on the conservative Fox News cable channel as he hoped to bounce back from a disastrous debate Wednesday, when he couldn't remember the name of the third of three U.S. government agencies he said he would abolish.

That has created an opening for former House Speaker Newt Gingrich to jump into the top tier of contenders in the latest polls of Republican primary voters and put himself forth as the conservative alternative to Romney.

Perry was briefly a front-runner after entering the race, but fell into the bottom tier of candidates after a series of weak debate performances. Wednesday's blunder was his worst moment yet, becoming the talk of American politics and fodder for television comedians.

National donors privately worry that he won't be able to survive the gaffe.

Cain, the former chief executive of Godfather's Pizza, avoided the early voting states on Friday as he continued to face questions about the sexual harassment allegations. He was in New York for fundraisers, foreign policy briefings and interviews with Fox News Channel and the New York Post.

Cain conceded on Fox that his campaign might have to moderate its approach to the allegations. He has strongly denied the accusations against him.

Cain has cast himself as the victim of a media smear campaign, currying favour with many conservatives who believe news coverage is biased in favour of Democrats.

"It plays to the victimhood strain, the aggrieved aspect of being a conservative in an allegedly liberal, elitist media world," said Marty Kaplan, a professor of media and politics at the University of Southern California. "Cain has played into that -- he gets the benefits of attention, and for his conservative supporters it proves what a grand antagonist toward the media he can be."

Audience members booed at Wednesday's debate when CNBC's Maria Bartiromo questioned Cain about the harassment claims. And they cheered when Cain pushed back.

But private polling suggests the harassment controversy has taken a bite out of Cain's once-solid lead in Iowa. And a new nationwide CBS News poll out Friday indicates he has lost support among women.

The CBS News poll, conducted Nov. 6-10 during the span of both crises, suggests a three-way tie for the nomination. The poll showed Cain with 18 per cent support among Republican primary voters and Romney tied with a resurgent Gingrich at 15 per cent.

The CBS News poll said Cain's support among Republican women has dropped since late October, from 28 per cent then to 15 per cent now.

Gingrich is the fiery Georgian who led the Republican Party's 1994 takeover of the House of Representatives after 40 years in the minority. He eventually lost his leadership post and left the House of Representatives after clashing with President Bill Clinton over taxes and an unpopular government shutdown.

Gingrich suggested that Republicans are still searching for a conservative alternative to Romney, who has held a steady though not breakaway lead in the polls and has run his campaign without major gaffes or problems. But Romney is viewed warily by conservatives because of his past support for abortion and gay rights and implementation of a health care reform plan in Massachusetts that Obama used as a model for his plan that Republicans loathe.

"The 85 per cent who have not chosen Mitt Romney, who have known him now for five years, I think are looking for a conservative activist who will stand firm and who will fight to change Washington," Gingrich told conservative radio host Laura Ingraham.

Gingrich, who saw most of his national campaign staff resign earlier this year, has ramped up his campaign efforts in recent weeks and is set to open a headquarters Saturday in South Carolina, which is the first southern State to hold a primary.