If Mr Johnson continues resisting pressure to resign, it is likely the Committee, which represents backbench Tories, would consider changing the rules.
Despite the political chaos, the Queen still held her weekly audience with the prime minister on Wednesday.
Sajid Javid, who along with Rishi Sunak resigned on Tuesday, delivered stinging attack on the PM earlier in the Commons, telling him "enough is enough".
He told the prime minister that being one of his ministers meant he was having to chose between "loyalty and integrity" and said he "will never risk losing my integrity".
Almost all of those who left government since Tuesday cited issues with Mr Johnson's integrity, referring to scandals such as Partygate and the more recent Chris Pincher controversy.
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