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 1 pm.
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.
