Donald Trump has decried the Obama-Turnbull refugee deal in an angry message posted on Twitter.

"Do you believe it? The Obama Administration agreed to take thousands of illegal immigrants from Australia. Why? I will study this dumb deal!" Mr Trump wrote.

Mr Trump accused Malcolm Turnbull of seeking to export the "next Boston bombers" to the US, the Washington Post has reported.

In what was meant to be a routine and friendly chat between the new president and Australia's prime minister, Mr Trump reportedly fumed at a deal Mr Turnbull had made with his predecessor Barack Obama to move 1250 refugees from Nauru and Manus Island.

"This is the worst deal ever," Mr Trump said, according to senior US officials quoted by the newspaper.

Mr Trump also revealed to Mr Turnbull that he had spoken to four other world leaders that day, including Vladimir Putin, and that "This was the worst call by far".

Mr Trump also bragged about the size of his electoral college win and his inauguration crowd during the call to Mr Turnbull, officials said.

The conversation was supposed to take an hour but Mr Trump hung up after 25 minutes, before the two could discuss other issues including Syria, according to the Washington Post.

"It was described to me as contentious, certainly, and at times hostile," Washington Post reporter Philip Rucker told ABC.

"The thing you have to understand about Donald Trump is that he is not a natural diplomat, he is not a politician."

Mr Turnbull today declined to comment on the conversation when asked at a press conference in Melbourne.

"I stand up for Australia in every forum, public or private," he said.

"It is better these conversations are conducted candidly, frankly, privately."

Mr Turnbull also insisted the deal over the asylum seekers would go ahead.

"That assurance was confirmed by the president's spokesman in the briefing room of the White House," he said.

Mr Turnbull yesterday pushed back against a report on the ABC that the deal was on shaky ground.

"We've got to raise the standards of journalism here," Mr Turnbull told 7.30 last night.

"We have a conversation between the prime minister and the president. The president gives an assurance. We have a confirmation of that assurance given by the (president's) spokesman given in the White House briefing room.

"That's what I'm basing my remarks on, and I think that's more reliable than some of the reports in the press."

The Australian embassy and the White House declined to comment on the testy exchange, but an official statement said the pair "emphasised the enduring strength and closeness of the US-Australia relationship".

Mr Trump's executive order last week put a temporary ban on refugees entering the United States from Iran, Iraq, Sudan and Somalia, where many of the Nauru and Manus asylum seekers hail from.

But a special provision in the executive order allowed for the deal Obama made with Mr Turnbull last year to still be carried out.