He said: “Thank you once again to friends and colleagues for your support in the third ballot – especially on my birthday!
“We’ve come a long way but we have much further to go.”
The International Development Secretary, whose support plummeted by 10 votes to 27 yesterday, suggested dirty tricks had taken place involving proxy votes and support being “lent” to other candidates.
He was understood to be in talks with third-placed Michael Gove about a possible pact to try to seize second place in today’s final round.
Mr Johnson won the backing of 143 of his party's 313 MPs yesterday
Their plotting could lead to a sensational final run-off between Mr Johnson and his arch rival Mr Gove.
Amid the acrimonious exchanges yesterday, a senior Tory peer likened the conduct of the contest for the party’s next leader to corrupt election practises in despotic Third World regimes.
“If this had happened in Zimbabwe last year I would have submitted a highly-critical report,” said polling expert Lord Hayward.
Mr Johnson won the backing of 143 of his party’s 313 MPs yesterday, up by 17 votes from the previous round.
His former Vote Leave comrade-in-arms turned bitter rival Michael Gove came tantalisingly close to overtaking second-placed Jeremy Hunt in the ballot.
The Environment Secretary won 51 votes, up by 10, compared to 54 for the Foreign Secretary on 54, up eight.
Home Secretary Sajid Javid managed to cling on with 38 votes, up by five from the previous round.
Tory MPs are braced for up to two more rounds today to determine who will face Mr Johnson in the final head-to-head run off decided by the party 160,000 grassroots members next month.
Mr Stewart, an unexpected star of the contest, saw his support plummet by 10 votes to 27 yesterday following performance in a live BBC clash that he publicly conceded had been “lacklustre”.
But during voting, he raised questions about the role of former chief whip Gavin Williamson, who has been marshalling support for Mr Johnson.
Mr Stewart accused Mr Johnson’s camp of “dark arts” by using up to 10 of his supporters’ proxy votes to lend to Mr Javid to knock him out, name-checking Mr Williamson as the man organising the plot.
“There are dark arts in politics and they’re done with proxy votes, they’re not done with someone saying would you please vote for this person,” the International Development Secretary said.
Asked to explain, he added: “They would give their proxy votes. For example, if you’re Boris, one of your whips would have four or five votes.”
Rory Stewart raised accusations of 'dark arts' and 'shenanigans'
Mr Johnson's team declined to comment on the allegations last night
He said: “I mean, he has people who have five or ten proxy votes, so some very interesting things could happen.”
Speaking ahead of the voting, Mr Stewart said an “enormous number of people” wanted him knocked out of the contest because the “message I’m bringing forward is too challenging.”
Asked if they could find a way of sabotaging him, he replied: “The might well and there’s a lot of talk about shenanigans going on.”
Mr Johnson’s team declined to comment on the allegations last night.
Bowing out of the contest, Mr Stewart said: “I am so moved and inspired by the support I have received over the last few weeks – it has given me a new faith in politics, a new belief in our country.
“I didn’t get enough MPs to believe today – but they will. I remain deeply committed to you and to this country.”
Jeremy Hunt is batting to stay in second place
“The stakes too high to allow anyone to sail through untested.”
Vowing to keep fighting in today’s final knockout rounds, Mr Javid tweeted after the vote: “Delighted to make it through to the final day of MP voting. Grateful for the support of many excellent colleagues. We can do this!”
A spokesman for his campaign team said: “Saj has been counted out his entire life and he has to do it again.
“Never count out Sajid Javid. He’s in it to win it.”