Former chancellor Rishi Sunak and Leader of the House Penny Mordaunt have emerged as the main contenders.
Mr Johnson was forced late on Sunday to admit he could not unite his warring party, seemingly surrendering to Rishi Sunak.
The former prime minister admitted he cannot unite the warring Conservative Party.
The SNP Westminster leader’s comments come after Boris Johnson’s dramatic withdrawal from the Tory leadership contest.
The former chancellor became the second candidate to declare their prime ministerial ambitions.