The Conservatives have agreed changes designed to speed up the contest to succeed Theresa May as leader.
Eleven MPs are still in the race, after junior ministers James Cleverly and Kit Malthouse withdrew.
Housing Secretary James Brokenshire said on Monday that some should consider pulling out because the party needed to find a new leader fast.
Former Chancellor Ken Clarke called the contest a "shambles" and said there were too many people running.
The deadline for contenders to put their names forward is 17.00 BST on 10 June.