Theresa May has promised to set a timetable for the election of her successor after the next Brexit vote in the first week of June.
The agreement follows a meeting between the prime minister and senior Tory MPs who are demanding a date for her departure from Downing Street.
If she loses the vote on her Brexit plan, already rejected three times, sources told the BBC she would resign.
Meanwhile, Boris Johnson has said he will run for leader once Mrs May goes.
The prime minister survived a confidence vote by Conservative MPs at the end of last year and party rules mean she cannot formally be challenged again until December.
But Mrs May has come under increasing pressure to leave Downing Street this summer, amid the Brexit impasse and poor results for the Conservatives in the recent local elections in England.
BBC political editor Laura Kuenssberg said senior sources had told her it was “inconceivable” the prime minister could remain in office if MPs rejected her Brexit plans for a fourth time.
