US President Donald Trump has praised Prime Minister Malcolm Turnbull for "telling the truth" about their phone conversation on the Australia-US refugee deal.

Key points: Reports surfaced of tense call between Mr Turnbull and Mr Trump regarding refugee deal

Reports surfaced of tense call between Mr Turnbull and Mr Trump regarding refugee deal Mr Turnbull refuted leaked information saying the call was "very frank" and "forthright"

Mr Turnbull refuted leaked information saying the call was "very frank" and "forthright" White House Press Secretary Sean Spicer said deal would be honoured "in some way"

Mr Trump called the exchange "very civil" in a tweet, adding that "fake news" media had lied about details of the exchange.

Loading

Following conflicting reports about whether or not the deal would proceed, White House Press Secretary Sean Spicer reiterated in his latest press conference on Friday (local time) that the US would honour the deal "in some way".

"We're going to vet these people in accordance with the agreement that happened and we'll continue to have further updates as we do," he said.

The deal to take refugees from Manus Island and Nauru was brokered between the Federal Government and the US in the closing weeks of the Obama administration.

Details of a tense phone conversation with Mr Turnbull, which Mr Trump reportedly described as "the worst by far", were published by the Washington Post on Thursday.

Mr Trump reportedly accused Mr Turnbull of seeking to export the "next Boston bombers" to the US, and complained that the deal was going to kill him politically.

Mr Trump followed up the conversation with a tweet in which he railed against the "dumb deal".

Mr Turnbull said he was disappointed the details of the call — which he described as "very frank and forthright" — had been leaked.

Sorry, this video has expired Trump has 'a lot of respect for Australia'

"The report that the President hung up is not correct," he said.

Mr Trump followed up his comments with some affectionate words towards Australia, telling a Washington function that: "I have a lot of respect for Australia, I love Australia as a country — but we have a problem."

He urged people not to "worry" about the "tough" phone calls he was having with world leaders.

"A lot of countries are taking advantage of us. Terribly taking advantage of us," he said.

On Thursday, Australia's Ambassador in Washington Joe Hockey met Trump adviser Steve Bannon and chief of staff Reince Priebus at the White House amid ongoing discussions over the agreement.

The White House said it assured Mr Hockey the refugee deal will be honoured "in some way", during what Mr Spicer described as a "cordial" and "candid" meeting.

The meeting came as Mr Turnbull claimed the deal would still be honoured by Mr Trump, who he described as "a big personality".

"I will leave others to comment on him, but clearly he is a very big personality," Mr Turnbull said.

A number of US senators had called Mr Hockey to offer apologies, including former presidential hopeful John McCain.

In a statement, Senator McCain described Australia's as "one of America's oldest friends and staunchest allies".