One of the contenders will challenge Barack Obama in November’s election.
The candidates will meet for the first televised debate of 2012 on Saturday.
Primary votes will be held this month in New Hampshire, South Carolina and Florida which could well shape the race for the Republican nomination.
Gingrich race row
Primaries and caucuses will take place in every US state over the next few months before the eventual Republican candidate is crowned at the party convention in August.
Former Massachusetts Governor Romney, who was declared the winner of last week’s Iowa caucuses, is the overwhelming favourite to win next Tuesday’s contest in his political heartland of New Hampshire.
Mr Gingrich was in New Hampshire on Friday trying to breathe new life into his campaign after a disappointing fourth-place finish in Iowa.
He said if Mr Romney was chosen as the eventual Republican nominee, President Obama would “laugh at him” in debates because of the similarities between Mr Obama’s healthcare reforms and laws passed by Mr Romney while governor of Massachusetts.
But as he tried to breathe new life into his White House hopes, former House Speaker Gingrich was forced on the defensive by a row over racially charged comments he reportedly made.
When asked what he would say if invited to speak at the National Association for the Advancement of Colored People [NAACP], Mr Gingrich took the opportunity to attack Mr Obama’s economic policies, calling him the “food stamp president”.
“I’m prepared, if the NAACP invites me, I’ll go to their convention and talk about why the African-American community should demand paychecks and not be satisfied with food stamps,” Mr Gingrich said, in a remark that trickled out in blogs on Thursday.
NAACP President Benjamin Jealous hit back that the majority of Americans on food stamps were not black.
“It is a shame that the former Speaker feels that these types of inaccurate, divisive statements are in any way helpful to our country,” Mr Jealous said.
Mr Gingrich said his comments had been subjected to “grotesque reinterpretation” and that he only meant that “every young American deserves a chance to have a job”.
Another Republican candidate, Rick Santorum, was criticised last week over remarks he allegedly made about black people.
The former Pennsylvania senator was quoted as saying he did not want to “make black people’s lives better by giving them somebody else’s money”.
Mr Santorum said his remarks had not been reported accurately.
Huntsman as ‘Mao’
On Friday, he risked the wrath of older voters by calling for immediate cuts to Social Security benefits.
“We can’t wait 10 years,” Mr Santorum said while campaigning in New Hampshire.
Meanwhile, Mr Huntsman – who served as US ambassador to China for nearly two years – expressed outrage over an ad targeted at his adopted daughters by a group supporting rival Ron Paul.
The ad, by NHLiberty4Paul, shows footage of Mr Huntsman with daughters Gracie, who was adopted from China, and Asha, adopted from India, when they were infants.
“American values. Or Chinese?” the ad asks to a soundtrack of Chinese music. It calls Mr Huntsman “the Manchurian Candidate” and ends with an image of him dressed as China’s former communist leader Mao Zedong.
Mr Huntsman, who is trailing in most polls in the Republican race, said: “What I object to is bringing forward pictures and videos of my adopted daughters and suggesting there’s something sinister there.”
Ron Paul said: “I haven’t looked at it, but I understand it’s an ugly ad, and I’ve disavowed it. Obviously, it was way, way out order.”
Most of the Republican candidates are focusing their efforts on the primary in South Carolina on 21 January.