"I have just been provided with a request for a meeting of the Parliamentary Liberal Party. It has 43 signatures," he tweeted.
I have just been provided with a request for a meeting of the Parliamentary Liberal Party. It has 43 signatures. As soon as they are verified by the Whips, which should not take long, the meeting will be called.
"As soon as they are verified by the whips, which should not take long, the meeting will be called."
Turnbull has said he will not stand in the contest, meaning the next prime minister will be either Peter Dutton, who submitted the letter, Foreign Minister Julie Bishop or Treasurer Scott Morrison.
Turnbull survived one attempt to knife him on Tuesday, winning a party room vote 48-35, but since then ministers have been defecting and a second leadership challenge is likely at noon (0200 GMT) Friday.
Dutton needs to prove he has majority backing, or 43 signatures from within the party's parliamentary group -- a requirement for him to force a second crack at the top job ahead of national elections due by mid-2019.
Reports on Friday said at least 40 lawmakers were onboard for a leadership change.  Turnbull, who accused Dutton and his supporters of bullying and intimidation, on Thursday said he would not contest a second leadership challenge and leave parliament, although he did not put a timetable on when he would go.