Mr Turnbull defeated his ex-home affairs minister 48 votes to 35 in a snap leadership ballot on Tuesday, but Mr Dutton is now working the phones ahead of a second tilt.

"I am not going to beat around the bush on that, I am speaking to colleagues," he told Melbourne's 3AW radio on Wednesday.

"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."

Read more: Turnbull v Dutton –  Who voted for whom?

It is understood Liberal MPs are being lobbied on a joint leadership ticket involving Treasurer Scott Morrison and Mr Dutton.

Mr Morrison told reporters as he left a health-related event in Parliament House: "We want a stronger economy to help people, that is what I'm focused on, nothing else."

He said the "sort of nonsense" being seen in Canberra would put efforts such as dealing with multiple sclerosis at risk.

If Mr Dutton can get the numbers the challenge could be as early as Wednesday or Thursday.

"Anything is possible," one Liberal MP told AAP.

Backers of Mr Dutton believe his support levels are quickly climbing.

"Now that the genie is out of the bottle, I'm not sure we can put it back," Liberal MP Craig Kelly told the ABC.

Mr Dutton has started a media campaign to reach out to Australian voters, calling for a royal commission on fuel and energy prices, and said he would consider removing the GST on electricity for families and pensioners.

He also pledged to cut Australia's immigration intake if elected leader.

"We have to cut the numbers back (but) I haven't got a number to give to you today," Mr Dutton told 3AW.

At least 10 ministers offered to resign after voting against the prime minister, but most were rebuffed and will remain on the front bench.

So far Mr Turnbull has only accepted the resignations of Mr Dutton and International Development Minister Concetta Fierravanti-Wells, who wrote a scathing letter criticising the Liberal party for "drifting too far to the left".

Mr Turnbull, who has not made any media appearances on Wednesday, has called for unity after fending off the leadership threat.

"We've got to put 25 million Australians first. They hate it when we are talking about each other," he said on Tuesday.

But some Liberal MPs believe his position is terminal.

"I think there was a shift after the partyroom meeting with the offers of resignation by a considerable number of ministers," Tasmanian Liberal Senator Eric Abetz said.

Meanwhile, at least three Nationals MPs, including Veterans Affairs Minister Darren Chester, are threatening to quit the coalition and move to the cross bench if Mr Dutton seizes power.

"All options are on the table in a volatile environment," Mr Chester told the ABC.

Victorian Nationals MP Damian Drum said if the Liberals do change leaders, they will need to redraft the coalition agreement.

A leadership change could also trigger an early general election, which could be tough for cash-strapped state Liberal branches still finalising their candidates.

Mr Dutton says he ran because he believed he was the best option to head off a Shorten Labor government.

AAP