Former Conservative leadership contender Esther McVey has thrown her support behind Boris Johnson’s bid.
Ms McVey – eliminated in the first ballot – told the Sunday Telegraph she was backing him because he had promised to deliver Brexit by 31 October.
Mr Johnson is the clear frontrunner to replace Theresa May but his rivals have insisted they will not drop out.
He is the only one of the six remaining candidates who will not take part in the first TV debate on Channel 4 later.
His team reportedly have reservations about its proposed format, but Mr Johnson has agreed to take part in the BBC’s debate on Tuesday.
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BBC political correspondent Ben Wright said there was “intense arm-twisting and lobbying under way” ahead of the second ballot of Tory MPs on Tuesday.
He said Health Secretary Matt Hancock, who pulled out of the leadership race on Friday, was understood to be considering whether to back Mr Johnson or Michael Gove.
Mr Gove finished third in round one behind Foreign Secretary Jeremy Hunt, but has told the Sunday Times he is the “comeback kid”.
The environment secretary also said he would be happy to serve under Mr Johnson, whose leadership bid he scuppered in 2016.
“I would absolutely work with Boris in any way that he wanted to work with me,” he said. “No question. It is a different time requiring a different approach.”
Mr Hunt insisted he had still not given up hope of winning in the final postal ballot of party members, despite being a distant second to Mr Johnson in the first round.
“I am the insurgent in this race,” he told The Mail on Sunday.
“I am in it to win it because we have to give the country better choices given the crisis that we’re in now.”
Home Secretary Sajid Javid said voters were looking for a “change” – something only he and Mr Johnson offered.
He told the Sunday Times: “We need change. And Boris is change. But I’m change too. And there are only two change candidates in the remaining six – and that’s Boris and me.”
He also took a swipe at Mr Hunt, who he said was “an asset to the party” but didn’t represent change.
Meanwhile fellow contender, Rory Stewart, responded to a Sunday Times headline saying that the leadership rivals were eyeing cabinet roles under Mr Johnson by tweeting: “This may be true of some contenders but it isn’t true of me.”
The international development secretary added: “I want to give members and the public a real choice of two quite different futures for the Conservative party. I don’t want to be in a Boris cabinet.”
Mr Johnson gained 114 votes in the first ballot – more than double his nearest rival, Mr Hunt.
Writing in the Sunday Telegraph, Ms McVey said she would “wholeheartedly support” Mr Johnson after he agreed to incorporate aspects of her “blue-collar conservatism” ideas – such as investing money into public services – into his plans for government.
She added: “He has promised to deliver Brexit on 31 October, deal or no deal, and has shown time and time again that he is a dynamic leader, capable of building a strong team around him that will deliver on his promises.
“Our country is crying out for strong, optimistic leadership and Boris is the man best equipped to take us out of the EU.”
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Tory leadership: Boris Johnson wins backing from Esther McVey}