Conservative MPs are due to choose the two men who will contest the final stage of their leadership race later.
The remaining field of four candidates will be whittled down to three in another secret ballot, with the result expected at about 13.00 BST.
There will then be a further vote to select the final two, one of whom will be elected leader by party members.
Boris Johnson topped Wednesday’s third ballot with 143 votes, ahead of Jeremy Hunt, Michael Gove and Sajid Javid.
International Development Secretary Rory Stewart was knocked out of the contest on Wednesday evening, after he secured the backing of just 27 Tory MPs.
Mr Johnson is almost certain to make the run-off of 160,000 or so Conservative members who will elect the next Tory leader – and prime minister – in a postal ballot, starting next week.
But the race to join the former foreign secretary in the final two remains too close to call.
Mr Hunt, the foreign secretary, led Mr Gove by just three votes in the third round of voting, with 54 and 51 supporters respectively.
Home Secretary Sajid Javid was in fourth place with 38 votes.
He has insisted he will not pull out of the race and it is all to play for. His camp is hoping to attract backers of Mr Stewart.
Mr Javid’s campaign manager, Tory MP Robert Halfon, said the home secretary was “the outsider” but that he had support from across the party and was also picking up votes from former supporters of other candidates.
Mr Stewart has not yet said who he will endorse. There were reports on Tuesday that he had held talks with Mr Gove about combining forces.
The BBC’s political editor Laura Kuenssberg said there were all kinds of possibilities regarding potential alliances and pacts between the candidates chasing Mr Johnson.
Work and Pensions Secretary Amber Rudd – who backs Mr Hunt – told BBC Radio 4’s Today programme she was not “resigned” to Mr Johnson becoming prime minister.
“We haven’t seen much of Boris,” she said, adding that there were 16 hustings coming up over three weeks, with plenty of opportunities for members to decide who would be the best prime minister and “not just a good campaigner”.
The leadership campaign has, so far, been dominated by Brexit – with the candidates criticising each others’ plans for getting the UK out of the EU by the 31 October deadline.
Mr Hunt told LBC he believed the EU was prepared to re-open the agreement they reached with Theresa May – rejected three times by MPs – if they found themselves dealing with the “kind of person they could do business with”.
He said the current Withdrawal Agreement containing the controversial backstop – an insurance policy to maintain an open Irish border – was “dead”, and could not get through Parliament.
But he said he was confident the EU would listen to the UK if it came up with technological alternatives to the backstop, which they knew commanded the support of MPs.
“If you give them the kind of prime minister they think they can do business with, who is going to be fair and tough, then my reading of this is they do want to solve this,” he said.
Mr Gove told LBC there were always “twists and turns” in a leadership race, but he was “hopeful” of making it to the final two, given his breadth of support amongst Tory MPs.
While he had not spoken to Mr Stewart since his elimination, he said “having his support would be brilliant”.
Although Mr Johnson had “formidable qualities”, Mr Gove said he felt he would be a better prime minister than his former cabinet colleague and fellow Brexiteer.
“Boris Johnson has communication skills a plenty but when it comes to a forensic examination of Jeremy Corbyn’s programme, and a demolition of him in the House of Commons, I believe I would be better equipped than any of the other candidates.”
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– Has said he would consider a further delay to Brexit to achieve a better deal.
– Plans to negotiate a “fullstop” to the Irish border backstop plan. He wants a free trade agreement, similar to the deal between Canada and the EU.
– Would support a no-deal Brexit if he couldn’t get a better deal from Brussels.
– Would leave the EU with no deal, but it’s not his preferred option.
– Wants changes to the Irish backstop and proposes sending a new negotiating team to Brussels.
– Wants to make changes to the Withdrawal Agreement and thinks it’s possible to get them done by 31 October, but has not ruled out an extension.
– Would focus on making changes to the backstop. Would commission UK border force to work on solving the Northern Ireland border problem, paid for by the UK.
– Says he cannot envisage circumstances in which he would want to have another extension to the UK’s exit date and the country must be prepared for a no-deal Brexit.
– Wants to leave on 31 October, the deadline for Brexit set by the EU, with or without a deal. He admits a no-deal exit will cause “some disruption” but says the “way to get a good deal is to prepare for no deal”.
– Wants to remove the backstop from any deal and replace it with “alternative arrangements”.
– Says he would withhold the £39bn “divorce” payment the UK is due to give the EU as part of the negotiated deal. He says the money will be retained until there is “greater clarity about the way forward”.
TAX AND SPENDING
– Says he wants to replace VAT after Brexit with a lower, simpler sales tax.
– Wants to create the “most pro-business” tax regime in the world and put business at the heart of the revival of Britain.
– Says he would not use the tax and benefits system to give the already wealthy another tax cut.
– Says he would scrap the High Speed rail 2 project.
– As an entrepreneur, he wants to turn Britain into the next Silicon Valley, a “hub of innovation”.
– Pledged to slash business taxes to the lowest in Europe to attract firms to Britain after Brexit and reduce corporation tax.
– Has promised to break from the austerity of the past nine years by slowing the pace of debt reduction.
– Says this would free up about £25bn a year for spending priorities, including education.
– Other money would be spent on local government and efforts to tackle crime, including an increase in the number of police officers by 20,000.
– Pledges to cut income tax for people earning more than £50,000 by raising the 40% tax threshold to £80,000.
– Says it will benefit three million people and would cost £9.6bn a year.
– Plans to pay for the cut partly from a pot set aside by the Treasury for a possible no-deal Brexit, and partly by increasing employee National Insurance payments.
HEALTH AND EDUCATION
– Says he wants to ensure the NHS is “fully-funded, properly funded” and that funding is protected under law.
– Says he will spend £1bn extra on schools if he becomes prime minister.
– Mental health support in every school and a crackdown on social media companies that fail to regulate their content.
– A cut in interest rate paid on tuition fees.
– Long term plan to provide more funding for the teaching profession in return for a guarantee that no one leaves the education system without a “rigorous qualification” sufficient to work up to at least the average salary.
– Has suggested slowing down the rate of debt reduction, to release money for education.
– Wants to see a “multi-year, multi-billion-pound boost” to spending on schools to “change the life chances of so many young people”.
– Promises to raise spending on secondary school pupils to £5,000 each.
– Called the funding gap between some schools in cities compared to those in rural areas a “disturbing reality”.
– Has previously said money spent on the EU could be put into the NHS.