“I thought about calling in as Margaret from Fareham," the home secretary joked.
The former chancellor may have had an easy coronation, but he inherits a series of problems that will make his job very difficult.
The former chancellor has now amassed the support of more than half of the Conservative parliamentary party.
Former home secretary backs Johnson's rival, saying: "We are in dire straits. We need unity, stability and efficiency."
The Commons leader denied she was in talks to support Boris Johnson in return for a top Cabinet post.
The business secretary said the former PM had a "great deal of support".
The former chancellor pledged to “fix the economy, unite our party and deliver for our country”.
Tory leadership contender Suella Braverman is widely tipped to be appointed to Patel's role.
Sky-High Bills, Strikes And A Divided Party: The Challenges Facing Liz Truss As She Becomes The Next PM
The new Tory leader has a bulging in-tray that would be daunting for any prime minister to take on.
The former chancellor also declined to say whether he would vote down Liz Truss's economic plans if she becomes prime minister.