Penny Mordaunt has become the first Conservative MP to say they will run to replace Liz Truss as prime minister.
The Commons leader said she was standing to “unite our country” and win the next general election.
Rishi Sunak is also thought to be a likely candidate, and has got the most public nominations from MPs so far.
Boris Johnson has not ruled out a dramatic comeback, months after being forced out of No 10 after a Tory revolt.
The former prime minister has 39 MPs backing him, behind his former chancellor Rishi Sunak with 66 declared backers so far.
Ms Mordaunt, who like Mr Sunak failed in a bid to replace Mr Johnson over the summer, is further behind with 17.
She has been in and around government for the best part of a decade, and was briefly defence secretary under Theresa May.
The 49-year-old Portsmouth North MP backed Brexit and has worked hard to build up her profile with party activists, but did not get enough nominations to reach the members’ ballot last time.
Defence Secretary Ben Wallace has ruled himself out of the contest, adding he is “leaning towards” backing Boris Johnson.
Chancellor Jeremy Hunt has ruled himself out, along with Security Minister Tom Tugendhat and former cabinet minister Michael Gove.
Former Home Secretary Suella Braverman and International Trade Secretary Kemi Badenoch are thought to be considering bids.
Candidates to replace Ms Truss need support from at least 100 colleagues, meaning no more than three can get on the ballot.
Contenders have until 2pm on Monday to find 100 backers. If three reach the threshold, MPs will knock one out in a ballot on the same day.
MPs will hold an “indicative” ballot of the final two, with the winner then decided in an online vote of party members to finish on Friday next week.