Under intense pressure to call a second vote, Turnbull convened a party meeting on Friday after receiving a letter signed by the majority of party members calling for a change of leader.
"At the very least, the Turnbull government has been an average-to-good government, by most measures, brought down by internal divisions", said John Warhurst, a political scientist at the Australian National University.
Morrison became prime minister after winning a three-way contest by his party after they chose to spill Malcolm Turnbull from the top job.
Dutton, who Turnbull accused of bullying and intimidation in the move to knife him, pledged to provide "absolute loyalty" to Morrison.
One minister was so disillusioned with the push to oust Turnbull that he took to Twitter to apologize to the Australian people.
Relations between Trump and Turnbull started badly in February 2017 when Trump berated the Australian leader over a bilateral refugee agreement before abruptly ending their telephone conversation, according to a leaked transcript of the call.
Asked is Mr Morrison better for New Zealand than Mr Dutton would be as PM, she said: "Oh, we constantly make sure that we are the best representatives and advocates that we can be regardless of who we're advocating to".
"My honest congratulations to Scott Morrison on his election as leader of the Liberal Party", he said. While Dutton has promised to work with the moderates, some analysts believe the divisions are too great.
Australia uses the navy to turn boats back to Indonesia, or banishes refugees to remote immigration camps on the poor Pacific island nations of Papua New Guinea and Nauru.
"I look forward to it".
Turnbull's leadership was vulnerable because his government was trailing in opinion polls.
"'What the party voted for was that stable choice, moving to a new generation, and that means that we'll have continuity, but there will be points of emphasis and direction that we'll be consulting with our cabinet on".
The insider view is that a secret ballot is the way to settle the leadership, but the insider view has given Australia seven prime ministerships in a bit more than a decade.
Past year the deeply Christian Morrison attracted more controversy for opposing a bill legalizing same-sex marriage, even though it had strong support from his party.
"In one sense I think there would be continuity (in the economic portfolio), in another sense, (he'll be) trying to downgrade or shift any radical action on climate policy", he told AFP. But it may not be enough to save his government, though. One Nationals legislator has already said he will sit on the cross-benches, and possibly support the opposition.
A general election is due next year.
"He can heal the wounds that threatened to fracture the coalition government and allow the government time to prepare for an election", he said.