Sydney NSW, Australia

Australian Foreign Affairs Minister Julie Bishop will stand for leadership of the ruling Liberal party, local media reported on Thursday, after several ministers tendered their resignations and left Prime Minister Malcolm Turnbull clinging to power.

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Turnbull narrowly won a leadership vote on Tuesday against the former home affairs minister, Peter Dutton, and on Thursday offered to hold a second vote on Friday if he received a letter signed by the majority of the Liberal party.

Treasurer Scott Morrison will also challenge for the top job in any leadership vote, local media reported earlier.

Meanwhile, Australian Prime Minister Malcolm Turnbull vowed not to "give in to bullies" on Thursday in the face of a new leadership challenge, but said he will quit politics if his party no longer supports him.

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"I do not believe in that. I have never done that. I have never given in to bullies, but you can imagine the pressure it's put people under," Turnbull said.

(With inputs from agencies)