The Commons leader becomes the first Tory MP to declare her candidacy for the party leadership.
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, according to BBC estimates, with Ms Mordaunt on 17. Mr Sunak has 66 backers so far.
Candidates to replace Ms Truss need support from at least 100 colleagues, meaning to more than three can get on the ballot.