Scott Morrison has invited US President Donald Trump to Australia during a "very warm" phone call the day after becoming Prime Minister.

Mr Morrison, who fended off a challenge from Peter Dutton for the Liberal Party leadership on Friday, spoke to the US President on Saturday morning in a sign the new Prime Minister is keen to assure allies a week of turmoil in Australian politics poses no threat to international relationships.

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"Both underlined the strength and depth of our alliance and the unbreakable friendship between Australia and the United States," a spokesman for Mr Morrison said of the conversation.

"The Prime Minister invited the President to visit Australia. Both leaders agreed to stay in contact and to meet at an early opportunity.”