On Thursday, the Washington Post broke news of the tense call, with White House sources saying Mr Trump labelled a refugee deal between the US and Australia "the worst deal ever".

He also complained the call was "the worst by far" of any world leader that day, before abruptly ending the conversation 25 minutes into the scheduled hour, sources said.

This account was confirmed to Fairfax Media by an Australian cabinet minister, who described the report as being "broadly accurate".

Speaking on radio on Thursday, Mr Turnbull would only deny he had been hung up on. He said the call, which he described as "frank" and "forthright", ended courteously.

Late on Friday evening, Donald Trump responded to thank him for his comments.

"Thank you to Prime Minister of Australia for telling the truth about our very civil conversation," Mr Trump said.

Mr Trump accused "fake news media" of lying about the phone call.

However, Mr Turnbull did not publicly denounce the report, and government sources told journalists in Australia it was true.

Further government sources briefed numerous journalists on Thursday to say Malcolm Turnbull held his own in the phone call, which they characterised as being bullying.

At a prayer breakfast on Thursday, Trump also appeared to acknowledge he had been having "tough" phone calls.

"When you hear about the tough phone calls I'm having, don't worry about it," Mr Trump said. "Just don't worry about it. They're tough. We have to be tough.

"It's time we're going to be a little tough folks. We're taken advantage of by every nation in the world virtually. It's not going to happen anymore. It's not going to happen anymore."

Later, as diplomats in the US and Australia scrambled, Mr Trump held a meeting at the White House where he sent more mixed messages, implying Australia had taken advantage of the United States.

"A lot of people taking advantage of us, a lot of countries taking advantage of us, really terribly taking advantage of us," he said.

"We had one instance in Australia - I have a lot of respect for Australia, I love Australia as a country - but we had a problem where, for whatever reason, President Obama said that they were going to take probably well over a thousand illegal immigrants who were in prisons," he said.

"They were going to bring them and take them into this country. And I just said why?

"Why are we doing this? What's the purpose? So we'll see what happens. But a previous administration does something, you have to respect that."

Mr Turnbull has maintained the refugee deal - which will see 1250 refugees from Manus Island and Nauru taken to the US - will go ahead.