He plans to remain Prime Minister until a new Tory party leader is in place.
Boris Johnson is refusing to heed calls to let a caretaker premier ministre take over, as would-be successors are weighing up leadership bids.
There is growing pressure from senior Conservatives for Mr Johnson to step down immediately as Prime Minister and not wait for the election of a new leader.
Former Prime Minister Sir John Major was among those backing calls for Deputy Prime Minister Dominique Raab to be installed as a caretaker premier.