If everyone crosses this obstacle, the one with the smallest number of votes will come out of the race.
Johnson picked up 114 votes in the first round of voting by Conservative MPs in the leadership race on Thursday.
He said he only had six declared votes ahead of the poll, but "more than three times that" voted for him in the secret ballot.
The favourite for the contest is Johnson, the former foreign secretary and London mayor, who resigned from the cabinet over May's Chequers plan in 2018.
The contest is dominated by the issue of Britain's stalled departure from the European Union, with all the contenders promising to succeed where departing Prime Minister Theresa May failed and lead the country out of the bloc.
Andrea Leadsom, Esther McVey and Mark Harper didn't receive enough votes to progress and were eliminated from the contest. The included incumbent Foreign Secretary Jeremy Hunt, Environment Secretary Michael Gove, Home Secretary Sajid Javid, Health Secretary Matt Hancock, International Development Secretary Rory Stewart and former Brexit Secretary Dominic Raab.
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Another ballot of MPs will now be held next Tuesday, with further rounds to follow on Wednesday and possibly Thursday, until the field is narrowed to two. Parliament has rejected the divorce deal negotiated with the European Union three times and there is little agreement among lawmakers on Brexit.
Stewart, who has caught the imagination of the liberal commentariat with his inclusive speeches staged in public spaces, scraped through with 19 votes. We can win this.
"If we get to a point where a prime minister is intent on doing [a no-deal Brexit] the only way of stopping that prime minister would be to bring down that prime minister's Government".
The 30 votes which had been won by Mr Harper, Mrs Leadsom and Ms McVey are now up for grabs, with the remaining leadership candidates set to battle for support to ensure they can get over the threshold required in the next round. "If he continues like this he will lose the trust of his MPs, he will lose the trust of the members of the Conservative Party, and ultimately the trust of the electorate".
Wednesday's vote saw ten Conservative MPs support a Labour-led motion that would have given control of parliament's timetable to the opposition, and opened up the possibility of legislation that could prevent a no-deal Brexit.
The two will then face the second phase of the election, in which over 1.2 lakh members of the party will vote.
Candidates Esther McVey and Dominic Raab have both spoken of their willingness to enact a no-deal-Brexit, but Rory Stewart, an outsider whose somewhat eccentric campaigning style has proved unexpectedly popular, told the BBC: "No-deal is a bad thing. the best way of stopping no deal is to vote for a candidate who is against no deal".