LONDON -- Boris Johnson increased his lead Tuesday in the race to become Britain's next prime minister as one of his rivals was eliminated in a party vote, while upstart candidate Rory Stewart defied expectations to stay in the contest.

Johnson, a flamboyant former foreign secretary, won 126 of the 313 votes cast Tuesday in a second-round ballot of Conservative Party lawmakers that left five contenders standing. The total all but guarantees that Johnson will be one of the candidates in a runoff that will be decided by party members.

Dominic Raab, who tried to vie with Johnson for the votes of committed Brexit supporters, got only 30 votes Tuesday, three short of the threshold needed to go through to the next round.

Foreign Secretary Jeremy Hunt, Environment Secretary Michael Gove, Home Secretary Sajid Javid and Stewart all remain contenders in what is now effectively a race for second place and a runoff spot.

All five candidates were taking part in a live television debate on Tuesday evening, two days after Johnson skipped another televised debate despite being the front-runner.

Tory lawmakers will vote again Wednesday and Thursday, eliminating at least one candidate each time. The final two contenders will go to a postal ballot of all 160,000 Conservative Party members nationwide.

The winner, due to be announced in late July, will replace Theresa May as both party leader and British prime minister. May stepped down as party leader earlier this month after failing to secure Parliament's approval for her Brexit deal.

Johnson was already the front-runner after last week's first round of voting in a race that started out with 10 competitors. He has since been backed by several lawmakers who have dropped out. He is admired by many Conservatives for his ability to connect with voters, but others mistrust him for his long record of misleading and false statements, verbal blunders and erratic performance in high office.

Johnson added a dozen votes to his tally from last week, securing more than the combined total for the next three challengers: Hunt with 46 votes, Gove with 41 and Stewart with 37. Javid scraped into the next round with 33 votes.

Stewart has the most momentum, almost doubling his first-round tally, while Hunt and Gove barely increased their totals.

Stewart, Britain's minister for international development, calls himself the "anti-Boris," the pragmatist rival to populist Johnson. He has energized the contest with a combination of plain-speaking and quirkiness. He calls for compromises on Brexit, and accuses his rivals of peddling Brexit "fairy tales" about the amazing deals they will secure from the EU.

A former diplomat who once walked across Afghanistan and was a deputy provincial governor in Iraq after the 2003 U.S.-led invasion, Stewart is also the only contender regularly asked whether he has been a British spy. He denies it -- but notes that former spies are barred by law from disclosing their covert pasts.

Hunt and Gove are both considered experienced and competent ministers, but unexciting. Gove seems to have shrugged off the revelation that he used cocaine two decades ago.

Javid, the son of Pakistani immigrants, says he offers a common-man alternative to private school-educated rivals like Johnson and Stewart, although he was a highly paid investment banker before entering politics.

All the contenders vow they will succeed where May failed and lead Britain out of the European Union, though they differ about how to break the country's Brexit deadlock.

Johnson says the U.K. must leave the bloc on the scheduled date of Oct. 31, with or without a divorce deal to smooth the way.

The EU says it won't reopen the Brexit agreement it struck with May's government, which has been rejected three times by Britain's Parliament. Many economists and businesses say a no-deal exit would cause economic turmoil by ripping up the rules that govern trade between Britain and the EU.

Johnson's rivals are divided over how willing they are to contemplate a no-deal Brexit. Javid says a no-deal would be preferable to further delays, while Hunt warns it would cause "potentially severe economic disruption." Gove says he would be willing to postpone Brexit further in order to secure a deal.

Stewart has ruled out a no-deal Brexit and aims to get Parliament to back something very much like May's rejected Brexit agreement.

As he arrived for Tuesday's BBC debate, Stewart thanked supporters for keeping him in the race but said "there's a long way to go."

"I'm still very much the underdog in this race," he said.

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Danica Kirka in London contributed to this story.