Dominic Raab retired from the Tory leadership In the final ballot of the deputies, five candidates are available for the fight for the next prime minister.
Boris Johnson again scored the second ballot with 126 votes – 12 more than in the first round.
Jeremy Hunt, Michael Gove, Sajid Javid and Rory Stewart also received enough votes to get to the next round. 1
He also provoked controversy by refusing to suspend the parliament in order to thwart the MEPs' attempts to block a Brexit without a deal.
The surviving five candidates will attend a live BBC debate in central London at 8:00 pm CEST.
The next vote will take place on Wednesday, eliminating the lowest-ranked candidate.
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Mr. Hunt was second again in the last ballot of 313 Tory MPs with 46 votes – three more than in the first vote last week  Mr. Gove and Mr. Javid have also increased their support – by four and 10 respectively Votes on 46 or 33 votes.
But it was Rory Stewart, the International Development Minister, who made the biggest step forward, almost doubling his approval from 19 to 37 votes.
"Not Yet Done"
Tory MPs Gillian Keegan said Stewart is appealing to his colleagues for his "realistic plan" for Brexit, and his progress has shown that there is a "market for honest politicians".
"I think Rory is extraordinary, he has a star quality that is not often seen in politics."
Johnny Mercer, a follower of Mr. Johnson, said he was satisfied with his performance, but acknowledged that the competition is "not yet completed".
Defense Minister Penny Mordaunt, who supports Mr. Hunt for the top job, said he remains in a "strong" second place.
She told the BBC that the Secretary of State was "a serious candidate for a serious job".
Nicholas Watt of the BBC claimed to have learned from a source near Javid that he would not break the race even though he had the lowest number of votes.
Simon Hoare, one of the supporters of Javid, said he was "pleased" that the Home Secretary had made it to the next level.
He said, "Exclude emergencies," Mr Johnson would make it into the last two candidates and appealed to Tory MPs to "tactically" think about who should join him.
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Guy Opperman, who supports Michael Gove, said a frontrunner "had never won a Tory leadership competition" and he believed that MPs would eventually "band together" an alternative to Mr. Johnson.
He said Gove "found his way back into the competition" after days of negative headlines at the start of the campaign, after he admitted he had used cocaine as a journalist in the late 1990s.
As "A dedicated Brexiteer," he said, expecting Mr. Gove to pick up the vast majority of Mr. Raab's 30 supporters in the next round.
The remaining candidates face three more ballots this week, with the lowest-ranked MP eliminated until only two are left.
The last two names will then be sent to a postal vote of 160,000 Tory party members, starting on June 22, the winner is expected to be announced four weeks later.