Mitt Romney picked up another victory in the race for the Republican presidential nomination on late Saturday as he confidently carried his party's caucuses in the northwestern state of Washington.

Romney declared victory in the contest after returns showed him far ahead of former senator Rick Santorum and Texas congressman Ron Paul, who vied for second place.

With 80 per cent of the ballots counted, Romney was ahead with 36 per cent of the vote, Paul ran a distant second with 25 per cent while Santorum was close behind with 24.6 per cent.

Former House speaker Newt Gingrich was fourth with just 10.9 per cent of the ballot.

"I'm heartened to have won the Washington caucuses, and I thank the voters for their support," Romney said after most of the precincts had reported. "Every day that passes with Barack Obama in the White House is a day in which America's recovery from the economic crisis is delayed."

Party officials said there was record turnout for the caucuses, the latest state-by-state race to pick the Republican party's candidate to challenge Democratic President Barack Obama in November.

The candidates now head into Super Tuesday, next week's crucial contest in 10 states.

Romney and Santorum are seeking to harness momentum going into next week's balloting in Georgia, Massachusetts, Ohio, Oklahoma, Tennessee, Vermont and Virginia, Alaska, Idaho and North Dakota.

Romney held a brief rally on Saturday morning before leaving Washington state, which borders Canada.

Voters flocked to Saturday's caucuses, enthused that Washington state, which is usually little more than an afterthought in an election year, was attracting attention due to the tight race.

Kirby Wilbur, the state's Republican party chairman, said 21,000 voters had cast ballots and some counties had yet to return their results.

"This shows a high level of enthusiasm and excitement and shows how important the straw poll has been," he added.

His view was shared by first-time caucus-goer Erin Haick, who voted in a caucus at a Seattle high school.

"Usually it doesn't matter. It's just really exciting that Washington's caucus is important," Haick said.

The 30-year-old voted for Santorum as the former senator from Pennsylvania has been a "consistent conservative and I don't feel the same way about the other candidates."

A win in Washington is largely symbolic. Although the state has 43 delegates to the Republican Party convention, which will crown the nominee, these will be chosen at a later date and Saturday's results are non-binding.

To win the nomination a candidate has to secure a total of 1,144 delegates, so the results from Tuesday's votes in 10 states with about 400 delegates up for grabs are pivotal.

In the volatile race, Romney had won six states, Santorum four and Gingrich one before the Washington state contest. Romney has secured more than 150 delegates, with Santorum close to 70, according to a count by the website Real Clear Politics.

In a sign of how tight the delegate battle is, Santorum's lawyers filed a complaint over the allocation of delegates in Michigan.

But there was a further setback for Santorum on Saturday as he failed to get onto the ballot in some districts in Ohio, meaning he will not be eligible for 18 out of the 48 delegates in the state.

Romney campaign staff hit out at what they called ‘organizational incompetence,’ denouncing their main rival's slip up.

Santorum had ‘flunked’ a test of his organizational skills, Ben Ginsberg, national counsel for the Romney campaign, told reporters on a conference call.

"That is a failure that goes... to the organizational deficiencies that should give Republican voters great pause as we prepare to face Obama," he said.