Mr Dutton resigned from the cabinet after rejecting an offer to stay as Home Affairs minister, and refused multiple chances when questioned by reporters to rule out another challenge.
Malcolm Turnbull defeated Dutton in the party room ballot by 48-35.
Turnbull, trying to regain the initiative as speculation swirled over his future, began a meeting of Liberal parliamentarians on Tuesday by declaring the leadership of the party, and therefore the government, open to be contested.
Mr Hawke, the only federal Labor leader to have won four elections, was challenged during a recession but prevailed 66 votes to 44.
Even if Malcolm Turnbull survives a second challenge against Peter Dutton, he looks set to lose the election in a landslide to Labor's Bill Shorten, following 38 consecutive Newspoll losses with this challenge denting his already-crumbling authority.
"It is good to be in front of the cameras where I can smile and maybe show a different side to what I show when I talk about border protection", he said.
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New York-based PepsiCo will fund the deal with cash on hand and has committed to keep SodaStream in Israel for at least 15 years. Goldman Sachs and Centerview advised PepsiCo, while Perella Weinberg Partners gave advice to SodaStream.
Some of Mr Turnbull's strongest supporters, including Mr Pyne and Simon Birmingham, have been appearing in the media this morning to shore up the PM's position.
He said although most government lawmakers supported the target of reducing Australia's greenhouse gas emissions by 26 per cent below 2005 levels, that support was not enough.
IT has been a tough day for Peter Dutton.
"I have been the shadow minister for health and finance, I have been the health minister, the minister for sport and I have been the minister for workforce participation".
But it's understood Mr Turnbull is not accepting the resignations of a number of other ministers, including Cybersecurity Minister Angus Taylor, Assistant Treasurer Michael Sukkar and Assistant Minister to the Prime Minister James McGrath. I am proud of the fact that I got children out of detention. We have now moved nearly 400 people off Manus Island and Nauru and that is a significant achievement.
"I made a decision not because i had any animosity towards Malcolm Turnbull".
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The prime minister of Australia was fighting for his political life last night as conservative backbench MPs plotted to topple him.
Mr Dutton said the government must get both its "policies and message right" on power prices, immigration and its pressure on cities, the drought, health, education and aged care. "That's exactly what he's been a wrecker, and he needs to get out of the joint". I would like to contribute to public debates.
"We just need to have a stable leadership and we need to stop these challenges".
"Voters will do what they always do they react very badly to internal tensions, to disunity", Mr. Economou said.
"I have been in the parliament for 17 years and on the frontbench for 14".
"What is my next step, what is my job from here?"
Tough talks, no agreements at Merkel, Putin meeting near Berlin
Putin attended the wedding before heading off to Berlin for talks with German Chancellor Angela Merkel later on Saturday. Photos showed Putin dancing with the bride, who was dressed in traditional Austrian costume.