Updated

Fresh off a debate in which several of the candidates tried to expand the gap between themselves and President Bush, Republican 2008 White House hopefuls jumped back on the campaign trail Wednesday to take another stab.

Former Massachusetts Gov. Mitt Romney told a group of civic and business leaders that the U.S. image abroad has suffered from the perception that the United States invaded Iraq unilaterally.

"I do think that we have suffered over the past several years for a number of reasons, and I think you probably know what they are," Romney said, citing the absence of strong international support in the lead-up to the war.

• Click here to read more about Romney's remarks about Bush.

"There has been the perception that we have not been as open and participative with other nations as is our normal approach," he said.

The 10 Republican contenders spent the two-hour GOP debate Tuesday night pushing away from Bush policies as well as one another as they tried to map out their own ideas in an effort to win over voters in a crowded field of candidates.

"We want to make sure that we have the strongest candidate to go up and beat Hillary Clinton, or Barack Obama or John Edwards when the time comes. A good, active debate helps do that," Romney told FOX News from a campaign event in Bedford, N.H.

In an attack on Arizona Sen. John McCain, who has helped craft an immigration reform bill, former New York City Mayor Rudy Giuliani on Tuesday night referred to the immigration debate as business as usual in the nation's capital.

"It's a typical Washington mess," Giuliani said of the immigration bill Bush wants Congress to approve.

McCain supports the immigration reform plan under debate in the Senate while Romney opposes the permanent residency provision for illegal immigrations currently living in the United States.

"Senator McCain and I were able to distinguish ourselves on immigration in a way that will be lasting in people’s minds," Romney said.

Giuliani and Rep. Tom Tancredo, R-Colo., also went after McCain's position on the issue of how to address the 12 million illegal immigrants in the United States.

But McCain stood firm.

"For us to do nothing is silent and de facto amnesty," said McCain, using a word popular among critics of the legislation.

Other Republicans fired back.

"If they get across my fence, we sign them up for the Olympics immediately," said Rep. Duncan Hunter of California, a vocal opponent of the bill and a proponent of building more fencing along the U.S border with Mexico.

The debate fell back to criticism over Bush's decision-making, linking the president to distrust within the Republican party.

"The president ran as a conservative and governed as a liberal," Tancredo said. "That is what has really been the basis, I think, of the distrust that has developed among the Republican base. It's well founded."

One debate question asked the candidates what Bush's biggest mistake has been in office.

"Spending," said Sen. Sam Brownback of Kansas.

Rep. Ron Paul of Texas said: "The president ran on a program of a humble foreign policy, no nation-building and no policing of the world, and he changed his tune."

Former Virginia Gov. Jim Gilmore said the party had abandoned its conservative principles, while former Arkansas Gov. Mike Huckabee said Bush had failed to clearly communicate his positions.

"We went to Washington to change Washington, and Washington changed us," said former Wisconsin Gov. Tommy Thompson, once a member of Bush's Cabinet. "If we're going to spend money like as foolishly and as stupidly as the Democrats, the voters are going to vote for the professional spender — the Democrat — not the amateur spender — the Republican."

The GOP candidates clearly contrasted themselves with the man they hope to replace, even if it meant violating the cardinal rule of a Republican icon they routinely embrace. "Thou shalt not speak ill of any fellow Republican," former President Reagan used to say.

"I speak about three legs to the Republican stool being necessary to win a general election, which is a conservative base in terms of military, economic, family and family values," Romney said. "Giuliani talks about the two-legged stool."

FOX News' Carl Cameron and The Associated Press contributed to this report.