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The Washington Post has obtained what it says are White House transcripts of the president's first phone calls with the leaders of Australia and Mexico.

The transcript shows Mr Trump repeatedly blasting Mr Turnbull during their 24-minute call over the refugee-swap deal negotiated under the Obama administration.

The President described his conversation with Mr Turnbull as the "most unpleasant call" he had taken from world leaders that day. He had already spoken with Russian President Vladimir Putin, Japanese Prime Minister Shinzo Abe and German Chancellor Angela Merkel.

The tense conversation ended with Mr Trump reluctantly agreeing to honour the deal, but he described his call with Mr Putin as "pleasant" compared to his conversation with Mr Turnbull, which he said was "ridiculous".

Earlier this year, the Washington Post revealed key details of the tense phone call on January 28. The transcript published on Thursday shows Mr Trump struggled to understand Australia's asylum seeker policy, asking why the government didn't just free the detainees. He also expressed fears that Australia could be exporting new "Boston bombers" and repeatedly lambasted Mr Turnbull for the "stupid deal," which he said he "hated".

As part of his pleas for the new US administration to uphold the deal, Mr Turnbull said Australia would take "anyone" the US wanted it to take in return.

The conversation also confirmed Australia would take refugees from Central America as part of the arrangement, contradicting the Australian government's public insistence that the deal was not a swap.

"This is a very big issue for us, particularly domestically," Mr Turnbull said, according to the transcript. "It requires, in return, for us to do a number of things for the United States – this is a big deal, I think we should respect [the] deal.

"We will then hold up our end of the bargain by taking in our country 31 [inaudible] that you need to move on from ... we are taking people from the previous administration that they were very keen on getting out of the United States.

"We will take more. We will take anyone that you want us to take," Mr Turnbull promised as the President hit out at the "rotten deal".

"I am going to get killed on this thing," Mr Trump said.

"I will be seen as a weak and ineffective leader in my first week by these people. This is a killer," the President said, pointing out that it would contradict his hardline call for people from Muslim-majority countries to even be allowed to travel to the United States.

He also asked for Mr Turnbull's assurances that Australia would not be exporting terrorists.

"We have our San Bernardino's, we have had the World Trade Centre come down because of people that should not have been in our country, and now we are supposed to take 2000. It sends such a bad signal. You have no idea. It is such a bad thing," Mr Trump said.

At one point, Mr Trump asked: "Who made the deal? Obama?"

Mr Turnbull had to repeatedly explain Australia's border protection policies and the terms of the deal to Mr Trump, who appeared to struggle to comprehend the arrangement. The Prime Minister also several times corrected the President's claim that Australia would send 2000 refugees to the US. Mr Turnbull said the actual figure was 1250.

Mr Turnbull said the United States could decide to take only refugees who met its vetting procedures and that the "obligation is to only go through the process."

At one point he agreed with Mr Trump about the the prospect of the US vetting but then deciding to accept no refugees. However he added that he would expect the US to act in "good faith".

He described all the detainees on Nauru and Manus Island as safe and mostly "economic refugees" from Iran, Pakistan and Afghanistan.

"They have been under our supervision for over three years now and we know exactly everything about them," he assured the President. He added that if they had come by plane, they would have already been settled in Australia.

Mr Trump struggled to comprehend why Australia "discriminated" against people coming by boat and asked why the Australian government didn't just free the detainees if they were deemed safe.

Mr Turnbull said the policy was aimed at stopping people-smuggler networks selling dangerous sea voyages to Australia. And when he outlined Australia's harsh approach to asylum-seekers who arrived by boat – saying not even a Nobel prize-winning genius would be allowed to settle in Australia – Mr Trump praised the Australian leader as even worse than himself.

"That is a good idea. We should do that too. You are worse than I am," Mr Trump said.

"Malcolm, why is this so important? I do not understand. This is going to kill me," the President said at one point.

Mr Turnbull also boasted to the president that Australia had prioritised Christians from Syria.

"This is exactly what we have done with the program to bring in 12,000 Syrian refugees, 90 per cent of which will be Christians," Mr Turnbull said.

"It will be quite deliberate and the position I have taken – I have been very open about it – is that it is a tragic fact of life that when the situation in the Middle East settles down – the people that are going to be most unlikely to have a continuing home are those Christian minorities."

"We have a similar perspective in that respect," he told the president.

Both leaders rubbished German Chancellor Angela Merkel's open-door policy to accept refugees fleeing the Syrian conflict. Mr Trump suggested that Mrs Merkel regretted her decision.

"Look at what has happened in Germany. Look at what is happening in these countries. These people are crazy to let this happen. I spoke to Merkel today, and believe me, she wishes she did not do it. Germany is a mess because of what happened," he said.

Mr Turnbull told the President that it was another area on which they agreed.

"I agree with you, letting one million Syrians walk into their country. It was one of the big factors in the Brexit vote, frankly," he said.

Mr Turnbull also said the two men were similar because they were both "highly transactional businessmen".