New Australian Prime Minister Scott Morrison said on Saturday he had spoken with President Donald Trump and been congratulated by the US leader, who got off to a famously rocky start with former premier Malcolm Turnbull.

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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.

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".

However, Trump offered Morrison his congratulations on Twitter. "Congratulations to new Australian Prime Minister Scott Morrison. There are no greater friends than the United States and Australia!" he wrote.

Morrison in turn said on Twitter he had spoken to Trump.

"Had a great discussion with @realDonaldTrump this morning. We affirmed the strength of the relationship between the US and Australia," Morrison wrote.

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

University of Sydney political analyst Rod Tiffen said he did not expect the personal relationship between the two leaders to affect strategic relations.

"I don't think it will make much difference, America has all the initiative in this relationship," he told Reuters by phone on Saturday.

Morrison set to work on Saturday building a new Cabinet, although the only confirmed change so far is the appointment of his Liberal Party deputy Josh Frydenberg, the former energy minister, as treasurer.

One of his first tasks will be to try to heal a bitterly divided party that has a parliamentary majority of only one seat. Morrison has ruled out calling an early general election but will face his first electoral test with a by-election for Turnbull's seat in Sydney.

The harbourside electorate has long been regarded as a safe seat for the Liberals.

Morrison's victory marks the chance for a break from a decade of leadership clashes but ideological divisions in the party over issues such as climate change, energy policy, immigration and even globalisation remain stark.