The six Conservative MPs hoping to be the next party leader are set to face a second round of votes today.
The vote will come ahead of a live TV debate that will feature the front-runner and former foreign secretary, Boris Johnson.
Candidates need to gain at least 33 votes from MPs to remain in the race to reach the final run-off, which will see some 160,000 Tory members select the next Prime Minister.
If all candidates pass the 33-vote threshold, the one with the lowest total will be eliminated and by the end of the week, four of the six current contenders will be forced out, leaving the final two to go head-to-head for votes from the Tory grassroots.
Boris Johnson's podium was left empty on Sunday
International development secretary Rory Stewart's campaign was boosted by the backing of defacto deputy prime minister David Lidington.
Mr Stewart only secured 19 votes in the first round of voting, but is trying to position himself as the "change" candidate who can defeat Mr Johnson in the July run-off.
Home secretary Sajid Javid, who got 23 votes in the last round, is also insistent he is in with a chance as he emphasises his appeal as a fresh face for the Tory Party.
Mr Johnson, who topped the initial poll with 114 votes, refused to take part in hustings with journalists on Monday, but is set to join rivals for a candidates' debate on the BBC on Tuesday evening.
Mr Lidington, who had supported health secretary Matt Hancock before he quit the race, said Mr Stewart was the right person to best connect the Tory Party with the country.
The cabinet office minister told a pro-Stewart gathering in London: "I think there is a yearning in this country for political leaders who tell it straight to people.
"What Rory has done in his campaign is to demonstrate that there are no no-go areas in this country for him or for the party which he aspires to lead."
The remaining six candidates are; Mr Johnson, Mr Stewart, Mr Javid, Jeremy Hunt, Dominic Raab and Michael Gove.