But new polling shows a Dutton government would crash at the election to Bill Shorten, with voters picking the Labor leader over the ex-Home Affairs minister.

A defiant prime minister is holding onto his leadership with support from his two key lieutenants Treasurer Scott Morrison and Finance Minister Mathias Cormann.

Mr Dutton's supporters circulated a letter on Wednesday night calling for the party room to meet.

"I understand there's a petition. I understand that a couple of hours ago there were nine signatures on it," Liberal MP Jane Prentice told reporters on Wednesday night.

It was unclear how many MPs had actually seen and signed the letter and if any cabinet ministers were willing to shift their support from Mr Turnbull.

Mr Dutton admitted he's calling Liberals trying to win support for a second challenge after failing 48 votes to 35 in a snap leadership ballot on Tuesday.

The electorate, however, appears to be supporting Mr Turnbull.

A Morgan poll of more than 1,200 voters found they picked Mr Turnbull as the better prime minister over Mr Shorten, 52 per cent to 44.5 per cent.

But Mr Shorten thumped Mr Dutton 59 per cent to 36.5 per cent when voters were given the chance to pick between them.

"The iron laws of arithmetic confirmed my leadership of the Liberal Party," Mr Turnbull told reporters in Canberra on Wednesday.

He was flanked by Mr Morrison and Senator Cormann, who both gave him public votes of support.

"This is my leader and I'm ambitious for him," Mr Morrison said, giving Mr Turnbull a hug.

"I support the prime minister, Malcolm Turnbull," added Senator Cormann.

"I will continue to serve him loyally into the future."

Mr Dutton launched a media campaign on Wednesday morning, going on Melbourne radio to call for a royal commission into fuel and energy prices.

But Mr Morrison unleashed on Mr Dutton's plan to take the GST off electricity prices, calling it a "budget blower" that would cost $7.5 billion over four years.

Mr Dutton's push for another challenge lost some steam amid questions about his parliamentary eligibilitydue to public funding of childcare centres held under a family trust.

The prime minister said he took Mr Dutton at his word that he had legal advice he was in the clear, however the government is expected to double-check with solicitor-general advice.

Asked whether he anticipated another challenge, Mr Turnbull said: "No."

A parade of ministers who voted against Mr Turnbull were asked in parliament whether they supported him, and all answered yes.

A number had offered their resignations but Mr Turnbull only accepted those of Mr Dutton, International Development Minister Concetta Fierravanti-Wells and junior minister James McGrath.

Mr Shorten has written to the prime minister asking that all major decisions be paused until the leadership question is resolved.

Thursday is the last day of parliament until September 10, with the next scheduled Liberal partyroom meeting on September 11.

Australian Associated Press