Turnbull had overcome a first challenge to his leadership by winning a party-room vote on Tuesday.
However, media reports on Wednesday said Turnbull might still be deposed by party rivals.
Turnbull’s challenger for premiership is his former home affairs minister, Peter Dutton, who lost the initial challenge for leadership in the Tuesday party-room vote 48 votes to 35, Presstv Reported.
Dutton, who resigned his cabinet post after losing the vote on Tuesday, said on Wednesday that he had lobbied in parliament for support and was now confident that he would be chosen for leadership again.
The second vote could possibly be held as early as Thursday.
Turnbull had called the first vote himself in an effort to end disputes regarding his leadership.
A family dispute
Both Turnbull and Dutton hail from the ruling Liberal Party.
However, some party members believe Turnbull’s popularity among Australian voters has diminished and they support Dutton for prime minister.
Meanwhile, 10 cabinet ministers — Dutton included — have tendered their resignations.
Turnbull has accepted only two resignations, those of Dutton and International Development Minister Concetta Fierravanti-Wells. He insisted on Wednesday that the others had since “given me unequivocal assurances of continuing loyalty and support.”
The deputy leader of the Liberal Party and the foreign minister, Julie Bishop, has said Turnbull seeks to end the crisis.
“Malcolm Turnbull wants to heal the divisions and unite the party, so we can get on governing for the Australian people,” she has said.
In the past decade alone, three sitting PMs have been replaced by party rivals within their first terms.
Australia is due to hold general elections before May next year.