Prime Minister Malcolm Turnbull says he will step aside if he loses the support of the majority of his Liberal colleagues.
Mr Turnbull said he plans to hold another partyroom meeting Friday to settle the leadership crisis, but only if he receives a petition signed by a majority of Liberal MPs asking him to do so.
He said it was also crtical that to sit in Parliament are resolved before another leadership ballot.
"You can imagine the consequences of having a Prime Minister whose actions and decisions are questionable because of the issue of eligibility."
In an extraordinary press conference, the prime minister criticised rebel MPs within his party for staging an “internal insurgency”.
"I have never given in to bullies, but you can imagine the pressure it's put people under," he told reporters.
“They’re hard to stop,” he said.
“What we have witnessed at the moment is a very deliberate effort to pull the Liberal Party further to the right.”
If he loses support for his prime ministership, Mr Turnbull intends to quit Parliament, threatening the Coalition's one-seat majority in the House of Representatives.
"I believe former Prime Ministers are best out of the Parliament."