President Donald Trump and Australia's new Prime Minister have held their first phone call, less than a day after Scott Morrison took over the top job.

Mr Morrison tweeted on Saturday afternoon he had a "great discussion" with Mr Trump, reaffirming the strong ties between the two nations.

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He has also spoken to the President of Indonesia, Joko Widodo.

Earlier, the US President took to his favourite social media platform to declare the United States has "no greater friend" than Australia.

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Mr Morrison was sworn in as prime minister on Friday afternoon, replacing Malcolm Turnbull, after winning a Liberal Party spill over Peter Dutton and Julie Bishop.

The pair could meet face to face later this year, at the APEC summit in Papua New Guinea in November, and there is speculation Mr Trump could visit Australia on the same trip.

The US President has not travelled to Australia since taking office.

Mr Trump did not decide to take the next step and follow Mr Morrison on the social media platform, with the list of accounts he follows remaining steady at 47.

Mr Turnbull famously had a terse initial phone conversation with a newly inaugurated Mr Trump, with the President cutting the call short and later calling it "crazy" and "unpleasant".