UPDATE: Malcolm Turnbull has told journalists Australians don't like it when the party focuses on itself, saying the party room has "confirmed" his leadership.
The Prime Minister said they cannot allow internal issues to undermine their work.
"Disunity undermines the ability of any government to get things done."
He also said disunity would "create a real risk that Bill Shorten will become Prime Minister."
Scott Morrison has taken over Peter Dutton's Home Affairs super ministery.
Turnbull also emphasised the vote was a secret ballot while Julie Bishop called the vote an "overwhelming vote of support."
EARLIER: PETER Dutton has resigned as Home Affairs Minister after Malcolm Turnbull defeated him in a heated leadership challenge. But it's not over yet as the Prime Minister could face another spill from MPs.
Turnbull won the leadership vote by 48 votes to 35 and will remain Prime Minister.
Chief government whip Nola Marino said Mr Turnbull called a ballot in the Liberal Party room after declaring his leadership vacant, and Mr Dutton put his hand up to challenge.
Sky News political editor David Speers said the situation was a "humiliation" for Mr Turnbull.
"In parliament, he's going to be standing there in front of a backbench, a third, nearly half of whom don't support him," he said.
"Incredibly difficult to see how Malcolm Turnbull can recover from this."
While the challenge over the prime ministership was ostensibly about energy policy, the true source of the leadership tensions goes much deeper.
Mr Dutton was seen as an alternative leader who could better represent the conservative wing of the party, which is not interested in locking Australia into ambitious carbon emissions cuts.
EARLIER: MALCOLM Turnbull's support in the Liberal party room has collapsed and he is facing the prospect of a leadership challenge as early as this morning.
Mr Turnbull has gutted two of his own signature policies in the last 24 hours in an effort to save himself, removing the carbon emissions target from the National Energy Guarantee (NEG) and depriving the big four banks of his company tax cuts.
A senior source has told The Daily Telegraph Mr Turnbull is "in panic mode" and "clearly rattled" amid reports Home Affairs Minister Peter Dutton is considering launching a leadership challenge at today's Liberal party room meeting, which starts at 9am.
The Australian says nine of Mr Turnbull's 18 Liberal cabinet colleagues have lost confidence in him, and the Prime Minister spent last night ringing MPs to shore up support.
The only question appears to be whether Mr Dutton will strike immediately or wait until parliament returns on September 10. That would potentially coincide with Mr Turnbull's 40th consecutive Newspoll loss.
As you may recall, Mr Turnbull cited Tony Abbott's 30 straight defeats in the poll as one of the main reasons for toppling the former prime minister.
DODGING THE QUESTION
Appearing on the ABC's 7.30 program last night, Treasurer Scott Morrison refused to concede Mr Turnbull's position was under threat.
Mr Morrison fronted up to be interviewed by Leigh Sales because Mr Turnbull himself declined the invitation. Ms Sales asked whether there was a "legitimate threat" to the Prime Minister.
"I don't believe so, and the reason for that is we're getting on with the job and just announced another big change in terms of going forward with the ACCC," Mr Morrison responded.
"That doesn't mean there's not a leadership threat," fired back anchor Leigh Sales.
"Well no one's calling me about it."
For the next few minutes, Ms Sales repeatedly asked the Treasurer where the source of the destabilisation was coming from, but he refused to offer up any suggestions.
"I don't know. I would have to ask you and the media who are reporting it," he said.
"Whoever is talking to the papers would know the answer to that question, but I wouldn't. Clearly, some people are talking to each other and they are talking to the media, so that's just obvious."
Asked again why he thought there were rumours of an impending leadership spill, he said: "I don't know because I'm not part of it. You would have to ask them."
IS DUTTON ELIGIBLE?
Meanwhile, a report late yesterday afternoon cast some doubt over Mr Dutton's right to sit in parliament.
Constitutional law experts told Ten the Home Affairs Minister could be disqualified from parliament over his business interests, Ten Eyewitness News reported.
In his parliamentary register of interest, Mr Dutton lists himself as a beneficiary of RHT Family Trust - along with his wife and children.
According to ASIC documents, the business owns two child care centres in northern Brisbane.
Under a law change Mr Dutton voted for, those centres have been receiving direct subsidies from the government since July 2 this year.
But Ten notes that, under Section 44(v) of the Constitution, any person with "any direct or indirect pecuniary interest with the Public Service of the Commonwealth" is disqualified from Parliament.
In April last year, the High Court ruled that then Family First Senator Bob Day was not validly elected to parliament, due to his breaching Section 44.
The Commonwealth had leased the office space at a building he owned in order to house his electorate office, the ABC reported.
Mr Day transferred the property to a family friend, but documents revealed there was an agreement that proceeds from the rent would go to a company he owned.
A spokesman for Mr Dutton told Ten: "Mr Dutton's legal advice clearly states there is no breach of Section 44."
But, if the case is referred by parliament, it could become a matter for the High Court to decide.
Meanwhile Hugh Riminton, the journalist who broke the story, has dismissed suggestions it was leaked to him by a Liberal Party member.
"We've been watching pecuniary interest matters with federal parliamentarians for a long time," he told The Project, noting his coverage of a similar story about Turnbull backbencher Barry O'Sullivan last year.
"The timing of all this talk of leadership issues is coincidental," said Hugh. "Many people won't believe thatm but its true."
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