OLYMPIA, Wash. — Mitt Romney won Washington state’s presidential caucus straw poll Saturday, capturing a strong portion of the vote of thousands of Republicans who crowded caucuses around the state.

With about 92 percent of the precinct votes counted Saturday night, Romney had nearly 37 percent of the vote, followed by Ron Paul with 25 percent. Rick Santorum was close behind with 24.4 percent and Newt Gingrich had nearly 11 percent of the vote.

Republicans had predicted up to 60,000 people would attend the caucuses. The results released Saturday were based on more than 47,000 votes counted from almost all of the state’s 39 counties. Romney has won 25 of the counties and was leading in King, the state’s largest, which was still counting votes. Paul won nine, and Santorum won four.

Romney said in a statement that the state’s voters “have sent a signal that they do not want a Washington insider in the White House.”

After the results came in, Paul addressed a lively crowd of supporters at a party along Seattle’s waterfront.

“The good news is we’re doing very well in getting delegates,” he said. “We do know that the strategy of building up delegates is sound.”

While the caucuses are a nonbinding contest, state Republicans say it could create momentum for the four candidates on their last stop before Super Tuesday, where voting takes place in 10 states.

Washington state will send 43 delegates to the national convention in Tampa in August, and the caucuses are the first in a multistep process to officially allocate 40 of those delegates to a candidate. Three additional are automatic delegates, and include the state party chairman.

Earlier in the day, precincts drew so many people that many locations were standing-room-only and one Eastern Washington location turned away hundreds of people.

Tony Benegas, a member of the Benton County Republican Committee who ran the Kennewick caucuses, estimated up to 800 people were turned away from Three Rivers Convention Center. Organizers had expected about 1,500 people, but many more showed up Saturday morning.

Benegas said the caucuses were run by volunteers, and there weren’t enough to check everyone in. He said there also weren’t enough computers to help voters look up their registrations, and the rooms were full.

“There’s not much we can say, except, ‘We’re sorry,'” he said. “We tried to get as many people in as possible.”The four presidential candidates vying to take on President Barack Obama have all visited the state in recent weeks, some twice. Paul was the only one still in the state on Saturday, though he lost at a precinct he had visited Saturday morning, coming in third behind Romney and Santorum.

Even though Washington state has voted exclusively Democratic in presidential elections since backing Ronald Reagan in 1984, state Republican chairman Kirby Wilbur said the strong turnout was a signal that “Democrats should be concerned.”

“We will not lack for energy or enthusiasm, at least on our side,” he said.

In the liberal stronghold of Seattle, hundreds gathered at the Labor Temple in the Belltown neighborhood. High school senior Cole Thomas said he was supporting Paul because of his pledges to bring troops back home from overseas, and because he agrees with his Libertarian stances on things like drug policy and other issues.

“I’m big on small government,” the 18-year-old said.

In Olympia, roughly 500 people packed the Red Lion Hotel’s basement conference room. The crowd exceeded the expectations of caucus organizers, as evidenced by a shortage of chairs at the site.

“It’s nice to see people get off the couch and think their vote is worth something again,” said Bruce Runyon, a mechanical custodian who supports Romney.

The large crowds were in spite of reports of people in King County and elsewhere receiving robocalls falsely claiming the caucuses had been cancelled. The state party said it was investigating the source.

Several hundred people packed the cafeteria at Phantom Lake Elementary School in Bellevue, where small groups debated issues of immigration, state budgets, transportation, abortion and other issues. Supporters backed a range of candidates, but there was one prevailing theme: beat Obama.

Timothy Rietveld, 57, a bank credit officer, said he voted for Romney, though “my heart is for Santorum.”

“I picked Santorum early as my dark horse, but I think at this point that Romney is the most electable, and the primary goal is to beat Obama,” said the Bellevue resident.

This is the first year since 2004 that Republicans won’t use a presidential preferential primary in addition to the caucuses. The primary was canceled this year for budgetary reasons, as was the one in 2004.

Up until 1992, the state relied solely on caucuses. But after 1988, when backers of television evangelist Pat Robertson swamped the meetings and ultimately took the nation’s largest Robertson delegation to the GOP convention in New Orleans, the Legislature quickly moved to create a presidential primary.

Previously, Republicans split delegate allocation evenly between the primary and caucuses, but this year they will solely use the caucuses.