Further rounds of voting are scheduled and the Conservatives should be down to their last two candidates by the end of Thursday
The field of contenders vying to become Britain's next prime minister narrowed to six on Friday when Health Secretary Matt Hancock withdrew from the contest.
The 40-year-old, who is against leaving the European Union without a deal, pulled out saying he was not in a position to win following Thursday's first round of voting.
Former foreign secretary Boris Johnson, a Brexit figurehead who insists Britain must leave the EU in October "deal or no deal," topped the secret ballot of Conservative MPs by a landslide, winning 114 of the 313 available votes.
Hancock came sixth out of the seven to make it through to a second round on Tuesday next week, when at least one more candidate will drop out.
"I have decided to withdraw from the race and work out what is the best way to advance the values that I care deeply about," he told the London Evening Standard newspaper.
"It is clear that I can't win from here," he said, having received 20 votes -- three more than the minimum threshold required to stay in the contest.
Hancock is one of the centre-right party's rising stars, a moderate widely seen as competent at his job and skilful with the media.
"I'm going to talk to all the other candidates and consider how best I can advance the values that I care deeply about," he said.
In Thursday's vote, Foreign Secretary Jeremy Hunt came second behind Johnson with 43 votes, while Environment Secretary Michael Gove was third on 37.
Following a televised debate on Sunday, candidates will need a minimum 33 votes to get through Tuesday's second round.
Further rounds of voting are scheduled and the Conservatives should be down to their last two candidates by the end of Thursday.
If Johnson does not lose votes next week, he is guaranteed a place in the final two.
But he is taking flak from other candidates as the only one yet to confirm he will take part in Sunday's Channel 4 debate.
After hustings around the country, the party's 160,000 grassroots members will pick their new leader in a postal ballot.
The winner will be announced in the week beginning July 22 and then take over from Theresa May as prime minister.