Canberra: Prime Minister Malcolm Turnbull is fighting to retain his position as he faces a demand by a party rival for a second leadership challenge.
Turnbull is under pressure over poor polling and a push by conservative members of his party to replace him, BBC reported on Thursday.
On Tuesday, former Home Affairs Minister Peter Dutton lost an internal party vote by a slim 13-vote margin.
The Australian media reported that Turnbull was resisting Dutton’s calls for a second vote on Thursday.
The prime minister has now lost the support of three key backers, seen as a blow to his chances of remaining leader.
Amid a fast-moving leadership crisis, local media reported that Dutton could face an additional rival – Treasurer Scott Morrison – if Turnbull decided to step aside.
Dutton asserted that Mr Turnbull had lost a majority of his colleagues’ support.
Turnbull’s allies said Dutton had not secured the signatures of sufficient MPs to force a second vote.
Dutton and several other ministers have now resigned from cabinet, despite Turnbull’s invitation for most to stay on.
The crisis has thrown Australian politics into a state of upheaval, and attracted criticism from both government opposition and the public.
If Turnbull is ousted, he would become the fourth leader in just a decade to have suffered a party coup within their first term.
In a key development on Thursday, cabinet ministers Mathias Cormann, Mitch Fifield and Michaelia Cash told reporters that they had withdrawn their support for Turnbull.
“It is with great sadness and a heavy heart that we went to see the prime minister yesterday afternoon to advise him that in our judgement he no longer enjoyed the support of the majority of members in the Liberal Party,” said Cormann, the finance minister.
Cormann called on Turnbull to hold an immediate internal vote.