"Former prime ministers are best out of the parliament", he told reporters on Thursday. "The work of government continues".
"I think that one of the big tasks we'll all have is to explain to the Australian people why this situation has occurred, and then how we're going to unite and focus to go and win the election, which can be won. because we have a very strong track record". It's also an worldwide embarrassment for a nation that prides itself as a safe and stable democracy in which to invest.
It is unclear whether Mr Turnbull will retire from parliament immediately or stay on until the next general election.
Defence Industry Minister Christopher Pyne, a Turnbull ally, refused to say who he would be backing and hit out at disruptive elements inside his party.
He played down speculation that he might call an election before it's due early next year.
Morrison presided over Australia's economy as the government sought to return the budget to surplus and simultaneously cut personal income and small business taxes.
Goaded and abetted by the insatiable vampires in the right wing of his party and the media, Mr Dutton, however, rushed to demand an immediate second vote.
In a December 2014 cabinet reshuffle Mr Morrison moved to the social services ministry and began remaking his public image to broaden his appeal.
Asked if he expected another leadership challenge this week, Turnbull, who has pleaded for party unity, replied: "No".
"It was described as madness by many, and I think it's hard to describe it in any other way". So Turnbull's decision to quit meant Morrison could not be accused of disloyalty.
The Treasurer edged out Peter Dutton, 45 to 40 in a partyroom meeting in Canberra on Friday afternoon.
Dutton also faces challenges to taking the top job. Dutton later suggested that the crisis was driven by personalities rather than policy differences.
Greens leader Richard di Natale said the only option for Australia to develop a response to climate change was to vote the government out of office.
Speaking to the country for the first time since being elected by party members as Australia's 30th prime minister Friday, Scott Morrison said his priority in the coming days will be to address a drought that has struck the state of New South Wales. A by-election for Turnbull's Sydney seat of Wentworth can't be held for weeks, and Parliament returns on September 10.
Relations between Mr Trump and Mr Turnbull started badly in Feb 2017 when Mr Trump berated the Australian leader over a bilateral refugee agreement before abruptly ending their telephone conversation, according to a leaked transcript of the call.