LONDON — Rishi Sunak, a former chancellor of the Exchequer, stayed at the front of the pack of candidates vying to replace Prime Minister Boris Johnson of Britain after the first round of the Conservative Party’s leadership contest on Tuesday.
But Penny Mordaunt, a relatively little-known junior trade minister, finished a strong second in the vote among Conservative lawmakers. And she has opened a commanding lead among the party’s rank-and-file members, according to a new poll, which suggested she could soon supplant Mr. Sunak as the favorite.
In the secret vote, more akin to a papal conclave than a national plebiscite, 357 Conservative lawmakers cast ballots to elect their next leader, who will become the fourth prime minister of Britain in six years.
Six candidates remained in the race after the first round. Two were eliminated for failing to clear the minimum threshold of support from 30 members of Parliament, including Nadhim Zahawi, who replaced Mr. Sunak as chancellor after he resigned last week in a move that set the stage for Mr. Johnson’s downfall.
It was the first of multiple rounds of party ballots this week, designed to whittle the sprawling field down to two finalists. They will spend a hectic summer wooing the party’s membership — a larger, though still limited group — which will elect Mr. Johnson’s replacement in early September.
The quirky nature of the process has already produced some surprises: While Mr. Sunak was expected to be the front-runner, and won a respectable 88 votes, Ms. Mordaunt’s 67 votes placed her within striking distance of him. Liz Truss, the foreign secretary, emerged as the third top-tier candidate, with 50 votes.
In a poll conducted by the market research firm YouGov, Ms. Mordaunt, a paratrooper’s daughter who serves in the Royal Naval Reserve, holds a wide lead among members over Mr. Sunak, Ms. Truss and all other candidates.
Two younger female candidates — Kemi Badenoch, with 40 votes, and Suella Braverman, with 32 — got through, keeping their hopes alive but raising the prospect that the hard-line Brexiteer vote may coalesce behind Ms. Truss.
Tom Tugendhat, the chairman of Parliament’s Foreign Affairs committee, who is running as an outsider, also survived into the second round, with 37 votes.
Jeremy Hunt, a former foreign secretary who unsuccessfully challenged Mr. Johnson for leader in 2019, came in last with 18 votes. Mr. Tugendhat would hope to pick up some votes in later rounds from the centrist Mr. Hunt.
Mr. Zahawi, with just 25 votes, was perhaps the day’s biggest disappointment. He had been a rising star in the party, propelled by his energetic management of the government’s rollout of coronavirus vaccines last year.
But critics faulted him for acting erratically last week, first accepting a plum post from Mr. Johnson, then calling on him to resign only a day later. There were also questions about Mr. Zahawi’s business dealings, which led him to complain that he was the victim of a smear campaign.
In the early days of the campaign, with so many candidates jostling for attention, the debates have been scattered and not particularly substantive. Much of the action involved horse-trading between candidates, with rising competitors eager to win over the votes of those who dropped out.
To complicate the picture further, Mr. Johnson suggested that the process of replacing him could move more quickly if the second-ranked candidate bowed out after the initial rounds and the leader was elected by acclamation.
Downing Street later said that if the winner was chosen on Sept. 5, as planned in the timetable set out by the party committee running the election, Mr. Johnson would deliver his formal resignation to Queen Elizabeth II the following day.
Appearing at one of his last sessions of Prime Minister’s Questions, Mr. Johnson said he was “leaving with my head held high,” despite a drumbeat of scandals that eventually turned his party and his cabinet against him.
In a sign that his rivals are already beginning to turn the page on him, the leader of the opposition Labour Party, Keir Starmer, devoted most of his questions to pressing Mr. Johnson for his views on people who have non-domicile tax status in Britain.
That status is claimed by the wife of Mr. Sunak, Akshata Murty, whose father is the Indian technology billionaire Narayana Murthy. Mr. Starmer signaled that Labour would make the wealth of Mr. Sunak and his wife the centerpiece of its attack on him if he emerges as the next Tory leader.
Mr. Johnson has declined to endorse any of the candidates, saying that to do so might hurt their chances. But in a lively exchange with Mr. Starmer, he predicted that any one of them would be able to “wipe the floor” with the Labour leader, whom he lampooned as “Captain Crash-a-Roony Snooze Fest.”