SYDNEY (AFP, REUTERS) - Australia's new prime minister began his first full day Saturday (Aug 25) with a phone call to Donald Trump as he set about restoring faith in his "battered and bruised" government after a tumultuous week.

Scott Morrison was sworn in as the country's 30th leader late Friday after a bitter Liberal Party revolt against moderate Malcolm Turnbull driven by a hardline conservative faction.

The former treasurer, a Turnbull ally who upset right-wing challenger Peter Dutton in the internal party ballot, said he had had a warm chat with the US president.

"Had a great discussion with @realDonaldTrump this morning," he tweeted.

"We affirmed the strength of the relationship between the US and Australia."

Morrison said he shared with Trump the story of Australian soldier Leslie "Bull" Allen "who is a symbol of our 100 years of mateship".

Allen famously carried to safety 12 wounded Americans during an attack on Japanese positions at Mount Tambu in New Guinea during World War II in 1943.

Trump also took to Twitter to congratulate Morrison.

"There are no greater friends than the United States and Australia," he said.

The US leader got off to a famously rocky start with former premier Malcolm Turnbull. 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.

Trump described the refugee deal, negotiated by Turnbull and former President Barack Obama, as "dumb".

Morrison emerged as the surprise winner of a party-room vote to replace Turnbull after a week of political chaos in Canberra that marked the emergence of Australia's sixth prime minister in less than 10 years.

Morrison, the former treasurer under Turnbull, took over as leader of the Liberal Party, the senior partner in the conservative Liberal-National coalition. The coalition has consistently trailed the opposition Labor party in opinion polls in recent months and must call a new election by May 2019.

A representative from the prime minister's office said Morrison had invited Trump to visit Australia during what was described as a "warm" conversation.

On Saturday, Morrison began work on nailing down a ministerial frontbench after a series of resignations as he looked to put a torrid week of political manoeuvring behind him.

"There's a lot to do today, so I'm looking forward to getting there and making sure we get everything in place that we need to," he told Channel Nine television.

"The stability of government - that continues, and I'll be meeting with some colleagues today as we pull the ministry (cabinet) together and make some announcements about that over the weekend."

He said his first official visit as prime minister would be to the drought-stricken state of Queensland next week.

"I'm not pretending to know one end of a sheep from another, but I do know people are hurting in the country, and they have been hurting terribly," SBS News quoted him as saying.

Turnbull blamed Dutton, former leader Tony Abbott and other Liberal "insurgents" for destabilising the party in their challenge to his leadership and Morrison must decide whether they should return to the frontbench.

The internal bickering infuriated many inside the Liberal party and renewed public disgust towards the political class.

Morrison, an evangelical Christian known as "ScoMo", admitted the government had been "battered and bruised" by the turmoil and has vowed to get the focus back on the Australian people.

He said his top priority was to help farmers in New South Wales state struggling through one of the worst droughts in half a century.

With the government lagging in opinion polls and national elections due by the middle of next year, Morrison also has his work cut out fending off a resurgent Labor opposition.

"The voters of Australia are telling me loud and clear that the last week in politics has probably been the biggest farcical week ever in Australian history," Labor leader Bill Shorten said on Saturday.

"It's a different leader, but it's the same chaos and division."