Morrison, who also spoke by phone to Joko Widodo, president of Australia's neighbour Indonesia, may meet Trump in person in November at a Pacific Rim summit in Papua New Guinea. Trump is reportedly considering a visit to Australia on the same trip.
Australia's 30th prime minister spent his first full day in office in meetings to sort out his Cabinet, with the only announcement so far being that new deputy Liberal Party leader Josh Frydenberg would take over Morrison's role as treasurer. Speculation was mounting that incumbent Foreign Minister Julie Bishop could follow Turnbull by quitting politics, after her unsuccessful run at the leadership in Friday's party vote, in which Morrison eventually beat Home Affairs Minister Peter Dutton, 45 votes to 40.
Morrison made brief public comments Saturday before meeting in Canberra, the capital, with farmers battling a severe drought that is affecting Australia's most populous state, New South Wales, in particular.
"There are many challenges our country has — our economic security, our national security," Morrison said. "I had the opportunity this morning to speak with President Trump and President Widodo, (I) will say about that another time. But (the) really important meeting in our country right at the moment is dealing with the drought."
But while Morrison put on a positive and upbeat public face, many Australians were still seething after his elevation to the prime ministership by his party, in a vote initiated to try to boost the Liberals' chances of holding power in the next election.
Turnbull is the fourth prime minister — from both the conservative Liberal Party and more leftist Labor Party — to be dumped by his or her own party before serving a full three-year term since this modern trend of leader-swapping began in 2010.
Social media was still abuzz Saturday with widespread anger and dismay that the country had a new leader without the public having had a say.
Prominent actor Magda Szubanski, star of the hit 1995 movie "Babe," spoke for many when she tweeted: "Well, if it wasn't clear before, it is crystal clear after the events of this week...what the people want counts for zero. It doesn't matter who we like, who we vote for or what policies we want. It is ALL about politicians' own agendas."
Others were even more scathing, with many expressing a wish that the nation's politicians would concentrate on doing what they were elected to do — run the country — rather than become derailed by in-party factional fighting and, of course, leadership spills. Many urged Morrison to call an early election to let the public make its choice.
On a well patronized message board on the Australian Broadcasting Corporation website, a respondent identifying herself as Alana C. wrote: "Call an election and let's be done with the bulls(asterisk)(asterisk)(asterisk). Australians really don't care about your squabbles, we want you to do your damn job. You know, the one we work our asses off to pay you to do?"
While the Sydney Morning Herald newspaper lamented on Friday that Australian democracy was now "a laughing stock", humorists continued to gain mileage out of this latest leadership coup.
A meme widely spread on social media featuring American comedian Drew Carey said, "Welcome to Australia — where voting is compulsory and the results don't matter."
There was disquiet, too, within the Liberal Party. More than one Liberal member of Parliament attacked their former prime minister Tony Abbott — the parliamentarian seen as having engineered Friday's vote to topple Turnbull, who had himself replaced Abbott in the top job in the Liberals' previous internal coup in 2015.
Liberal lawmakers Andrew Laming and Warren Entsch urged Abbott to resign."I think his mission is accomplished," Entsch told News Corporation. "He has got rid of his nemesis. Everything there was purely about revenge."
Abbott, however, appeared unrepentant in a brief meeting with reporters in Sydney on Saturday, pledging to give Morrison his "total support."
- AP