Favourite son Mitt Romney revived his bid for the Republican candidacy for president Tuesday night, claiming victory in Michigan's primary vote over his chief rival Senator John McCain.

Romney had 39 per cent of the centre-right Republican vote, followed by 30 per cent for McCain, the Vietnam War veteran and one- time prisoner of war. By late Tuesday, 83 per cent of Michigan precincts had been counted.

"Washington is broken, and we're going to do something about it," Romney declared in remarks to the cheers of enthusiastic supporters. "Tonight is a victory of optimism over Washington-style pessimism."

Romney said in an e-mail to supporters that the win gave him the "momentum" for two votes coming up Saturday - the Nevada caucuses for both parties and the South Carolina Republican primary.

Third place in the Republican race went to former Arkansas governor and Baptist minister Mike Huckabee, 52, with 16 per cent.

Former New York Mayor Rudy Giuliani, 63, a frontrunner in last year's build up to the race for delegates, was a distant sixth place behind relative unknowns Ron Paul and Fred Thompson, and has put most of his hopes in the Florida primary on January 29.

For the centre-left Democrats, the race faded in importance after the national party refused to accept any Michigan delegates at its national convention in August in Denver, Colorado. The move was retaliation for the Michigan Democratic Party's defiance of the national party's guidelines for state-level presidential contests.

Republicans plan to only accept half of Michigan's delegate votes for similar reasons.

Tuesday night in Michigan, Democratic voters cast 56 per cent of their votes for Senator Hillary Clinton, who remained on the ballot after her chief rivals, Senator Barack Obama, 46, and former senator John Edwards, 54, had withdrawn from the Michigan race due to the squabble with the national party.

Obama and Edwards urged their Michigan supporters to check the "uncommitted" box, which was receiving 39 per cent. Both continue to contest the Democratic nomination, including the next vote Saturday in the south-western state of Nevada.

Democrats did not entirely cede the national spotlight to the Republicans Tuesday night, holding a closely watched debate that saw calls for reconciliation after a campaign blowup over race issues between Clinton and Obama.

The next big vote for Democrats is January 26 in a separate Democratic primary in South Carolina, which will offer the first vote in a state with a sizeable African-American population.

The campaign in both parties is likely to remain hotly contested into the February 5 "mega-Tuesday" when 23 states cast primary votes. The parties won't make an official candidate choice until their conventions in August and September, just two months before the November 4 presidential vote.

McCain, 71, a strong supporter of the war in Iraq and a hawk on national security issues, had edged out Romney a week earlier in New Hampshire, and had hoped to do well in Michigan based on his 2000 victory in the Michigan primary over George W Bush, who was the eventual nominee.

Romney, 60, a wealthy businessman whose father once governed Michigan, ran a campaign pitched to the increasing economic worries in the Midwestern state, home to the embattled US automotive industry. Michigan's unemployment rate of 7.4 per cent is among the highest in the nation and far exceeds the national average of 5 per cent.

According to an exit poll cited by the Detroit News, 55 per cent of Republican voters cited the economy as the most important issue influencing their decisions.

In his victory speech, Romney, a former governor of Massachusetts, mentioned his concerns about illegal immigration, pensions, tax breaks for middle-income Americans and the country's dependence on foreign oil.

He laid claim to the legacy of previous Republican presidents Ronald Reagan and George Bush, but did not mention current president George W Bush, whose low approval ratings have made him somewhat of a pariah in the Republican race.

McCain accepted his defeat, saying he had gotten "pretty good at doing things the hard way."

"We don't mind a fight," he said, "and we're in it."