"I now await a letter with signatures of a majority of the party room. That’s 43. If I receive that I will convene a new party room meeting," he said at a press conference.
"If the motion is carried I will treat that as a vote of no confidence and I will not stand as a candidate in the ballot," he assured reporters.
This comes after resigned Liberal home affairs minister and a rival of the Prime Minister Peter Dutton called for a new closed-door party meeting, in a fresh challenge against Turnbull.
"A few minutes ago I spoke with Malcolm Turnbull to advise him I believed the majority of the party room no longer supported his leadership. Accordingly, I asked him to convene a party room meeting at which I would challenge for the leadership of the Parliamentary Liberal Party," Peter Dutton tweeted.
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Turnbull announced that the lower house of parliament had been adjourned at Dutton’s request and that he had asked the solicitor general to consider whether his rival was eligible to sit in the House.
The Australian government has been in turmoil after an exodus of ministers emphasized Turnbull’s waning support in his own party, which is a senior member in the ruling coalition. He narrowly won a leadership vote on Tuesday, initiated by Dutton.