Australia's Prime Minister Malcolm Turnbull says his phone conversation with US President Donald Trump this week was "cordial" but "very frank" as Trump reportedly expressed his anger over the proposed refugee deal between the two countries.

The deal was signed by Turnbull and the previous Obama administration late last year, and requires the United States to take in around 1,200 asylum seekers from Australia's offshore detention centers on Nauru and Manus Island.

Information leaked earlier in the week, and first published by the Washington Post, revealed the President described the 25-minute phone call with Turnbull as his "worst of the day", reportedly cutting it short by 35 minutes.

On Friday morning, Turnbull admitted the call was "forthright" and said the president was a larger-than-life character.

"He's clearly a big personality," Turnbull told radio journalist John Laws on Friday.

"I note that his official spokesman described the conversation as a cordial one this morning.

"I can say that it was very frank, it was forthright."

Trump made his feelings known about the refugee deal publicly on Thursday when he publicly Tweeted his displeasure: "Do you believe it? The Obama Administration agreed to take thousands of illegal immigrants from Australia. Why? I will study this dumb deal!"

Turnbull told the Australian media that the refugee deal would go ahead despite the President's strong words.

"As I've said, the President made a commitment to honor the deal which had been entered to by his predecessor. That's been confirmed now several times," Turnbull said on Friday.

"It's very important that it goes ahead because it will enable us to secure resettlement options for a number of the people on Nauru and Manus Island."

But the testing week for Australian-US relations was heightened further overnight, when the President's press secretary, Sean Spicer twice referred to Turnbull as "Prime Minister Trumbull", while the White House continues to backflip on whether or not the deal would proceed.

The President's attitude came as a shock to political experts across the world, as Australia has long been considered one of America's staunchest and oldest allies. Australia is also one of the Five Eyes intelligence alliance members along with Canada, New Zealand, the United Kingdom and the United States.

The leaded reports of Trump's candid phone call to Turnbull were picked up by major news outlets around the world, including CNN and the BBC.

Despite the worldwide reaction to the Turnbull-Trump phone call, former Australian Prime Minister Kevin Rudd said he believes the bilateral relationship was "big enough, old enough and ugly enough" to cope with the minor "snafu".

"(The relationship) been around for the better part of 100 years - in fact it's 100 years this year since Australians and Americans first went into battle with each other on the Western Front," Rudd told CNN from Abu Dhabi overnight.

"I think this snafu will blow over and we'll get back to the fundamentals of the relationship. On that, both sides of politics in the US and in Australia remain deeply committed.

"The bottom line is neither of us, you or I, were party to the actual conversation itself, so we'll let the two principals place their accounts of the call on the record.

"The fundamentals of this alliance have survived 14 US presidents, 14 Australian prime ministers, both sides of politics, and will keep going in the future because we have mutual interests at stake."

However former Australian Ambassador to the United States, Kim Beazley, said he would be "surprised" if the United States approves all asylum seekers as part of the deal, considering the "extreme vetting" promised by the White House.

"I'd be most surprised if absolutely every one of the (asylum seekers) was seen as acceptable," Beazley said.

source: Xinhua