Turnbull said Dutton had told him he would not challenge for the party leadership.
He's made good on that nearly immediately after the failed coup and resigned from his position as Minister for Home Affairs.
With both leadership positions spilled, the foreign affairs minister Julie Bishop's position as deputy Liberal leader was also opened, but she was the only one to nominate and was therefore re-elected.
Mr Turnbull's supporters say all the Prime Minister can do is "keep steering the ship".
Energy bills rose by up to six times the average wage rise previous year according to the Australian Bureau of Statistics.
The change would have followed on from a string of changes at the top of Aussie politics, which began when Julia Gillard ousted Kevin Rudd as leader of the Labor party in 2010. He later returned the favour and stormed back to power in 2013 shortly before losing the election to Tony Abbott's Liberal/National coalition.
"In relation to media stories today, just to make very clear, the Prime Minister has my support and I support the policies of the government", Mr Dutton tweeted.
Australian Prime Minister Malcolm Turnbull will recontest his position.
Malcolm Turnbull on Monday conceded that he could not get legislation through the House of Representatives where his conservative coalition holds only a single-seat majority.
A senior political figure described Mr Turnbull as being in "panic mode" and "clearly rattled" about the amount of support he has lost.
Mr Turnbull insisted he enjoyed the confidence of his party room - a claim echoed by several Cabinet ministers.
Labor frontbencher Anthony Albanese said the prime minister should call an election, if he survives the week.
"That is what people are telling me and that is what the government wants to do", he said. However, Mr Turnbull has consistently rated higher than Bill Shorten as preferred prime minister.