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A government lawmaker said on Wednesday he was planning a second challenge against Australia's prime minister after losing a leadership ballot, ensuring that Australia's political instability continues.

Prime Minister Malcolm Turnbull called on his government to unite behind him after lawmakers in the ruling conservative Liberal Party chose to keep him as their leader 48 votes to 35 in a ballot on Tuesday.

Turnbull surprised his enemies by calling the ballot before his challenger Peter Dutton had had time to lobby colleagues for support.

But Dutton confirmed that he was now sounding out support for a second challenge.

"I am not going to beat around the bush on that, I am speaking to colleagues," Dutton told Melbourne Radio 3AW.

"You don't go into a ballot believing you're going to lose, and if I believe that a majority of colleagues support me, then I would consider my position," he added.

Dutton has dashed Turnbull's hopes of unifying the conservative coalition under his leadership ahead of general elections due by May.

Dutton also used various media interviews on Wednesday to suggest new policy directions, including reduced tax on electricity bills and reduced immigration.

Turnbull suggested he still had the support of a majority of his party.

"The iron laws of arithmetic confirmed my leadership of the Liberal Party," he told reporters on Wednesday at a joint news conference with Treasurer Scott Morrison and Finance Minister Mathias Cormann.

Both ministers also declared their support for Turnbull.

Australia has had years of political instability since Prime Minister John Howard lost power in 2007 after more than 11 years in office. No prime minister has lasted a full three-year term since. They have all been thrown out of power by their own parties in the face of poor opinion polling.

Darren Chester, a minister in The Nationals party, the junior coalition partner, has threatened to take away the government's single-seat majority in the House of Representatives if Turnbull was deposed.

Chester said he and other lawmakers were considering quitting a government that was not led by Turnbull, which could force an election.

"I know of other colleagues who are deeply worried about" Turnbull being overthrown, Chester said.

Dutton quit as Home Affairs Minister after Tuesday's challenge failed.

Another 10 ministers who supported Dutton's challenge have also offered their resignations, but it is not clear how many the prime minister has accepted.

Turnbull said Dutton's was the only senior minister's resignation he accepted. It was not clear if Turnbull had accepted the resignations of junior ministers outside Cabinet.

"What I'm endeavoring to do is to obviously ensure that the party is stable, to maintain the stability of the government of Australia. That's critically important," Turnbull said.

"So the Cabinet ministers, apart from Peter Dutton, of course, who came to me and told me that they had voted for Mr. Dutton in the leadership ballot, have given me unequivocal assurances of continuing loyalty and support," he added.