Penny Mordaunt was racing to meet a threshold of 100 supporters on Monday, hours before a cut off which could see Rishi Sunak become the UK’s next prime minister.
The Conservative leadership candidate, who is leader of the House of Commons, has so far received the public backing of around 25 politicians. More than 150 have thrown their weight behind Mr Sunak.
Should she fail to hit the threshold by 2pm, Mr Sunak will become the country’s new prime minister, its third in eight weeks. If she makes it on to the ballot, the party's members will select the winner on Friday.
Her chances received a boost late on Sunday when former prime minister Boris Johnson announced he would not be entering the race.
Ms Mordaunt said Mr Johnson had put “country before party” by deciding against running in the race to replace Liz Truss.
She tweeted: “In taking this difficult decision last night Boris Johnson has put country before party, and party before self. He worked to secure the mandate and the majority we now enjoy.
“We should put it to good use, and I know he will work with us to do so.”
Conservative MP Damian Green has said he is confident Ms Mordaunt will reach the required number of endorsements to enter the race against Mr Sunak to be next leader of the Conservative Party.
He told BBC Radio 4's Today programme: “There are a lot of people who weren't declaring publicly what they were doing, I mean, indeed, Penny's numbers are well above the published figures already.
“It's certainly way, way above the published number and we're confident of getting to 100 before the deadline of 2pm and putting the case to colleagues that Penny is the person best positioned to unify the party.
“She's got support from all wings of the party already and we can then get on with the important job for the country of the various serious problems we're facing.”
However, Paul Goodman, the editor of Tory news website Conservative Home, warned Ms Mordaunt not to drag out her campaign.
“I have to say to Penny Mordaunt, for the good of the Conservative Party and the country, just don't push it because look at the figures,” Mr Goodman told the Today programme.
“Rishi Sunak, according to our count and other counts that are similar, has got 155 supporters — 179 is half the parliamentary party so he's really almost there.”
However, he warned Mr Sunak will face “enormous problems”, including the “disastrous legacy” left by his predecessor's brief administration.
“He's going to have to come to the Commons with his chancellor — I presume it will be Jeremy Hunt — with a whole programme of public spending cuts and tax rises just as a Labour government would now if it were there,” Mr Goodman said.
