Prime minister Malcolm Turnbull has announced he will call a party room meeting to decide the leadership if a petition shows it has the support of a majority of Liberal MPs and Senators.
Mr Turnbull said he will vacate the leadership and not stand if the petition has the support of his colleagues.
Health minister Greg Hunt and innovation minister Senator Michaelia Cash joined a number of other ministers in resigning from the Cabinet Thursday morning.
Their resignation came as Mr Turnbull faced increasing pressure to resign.
Mr Hunt backed former health minister Peter Dutton in the first leadership challenge earlier this week and could stand as his deputy in a second leadership ballot.
Treasurer Scott Morrison is expected stand for leader against Peter Dutton.
As deputy leader, Mr Hunt could choose his portfolio, including to remain in health.