"I am the world's greatest person that does not want to let people into the country".
The two leaders, both businessmen turned politicians sparred repeatedly about the status of a 2015 deal agreed to by President Obama to accept refugees now marooned on the island of Nauru and Papua New Guinea's Manus Island.
Despite reported friction between the two men, both Trump and Turnbull have repeatedly insisted that their countries enjoy a strong relationship. The prime minister corrects him and asserts that the deal is "quite consistent" with the president's first executive order restricting travel for people from seven majority-Muslim nations, according to the Post.
In exchange, Australia has pledged to take Central American refugees from a centre in Costa Rica - where the U.S. has taken in a larger number of people in recent years.
During the call, Turnbull noted that he and Trump have similar backgrounds as businessmen turned politicians.
The Post's report on Wednesday also included excerpts of Trump's January clashes with another foreign leader over immigration.
According to the transcript, Trump was under the impression that Australia would send its hardened criminals and terrorists to the USA from Nauru and Manus Island because they were in "a prison".
The Obama administration had agreed to accept some detainees on humanitarian grounds after intervention by the UN.
The Washington Post published transcripts of Trump's post-inauguration calls to Turnbull and Mexican President Enrique Peña Nieto. We should do that too. "And now I am agreeing to take 2,000 people", Trump said.
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"The only way that I can do this is to say that my predecessor made a deal and I have no option then to honour the deal", Mr Trump said. You can decide to take them or to not take them after vetting. "That is why they are in prison right now", he said. "They are not going to be wonderful people who go on to work for the local milk people" - apparently referring to American dairy farms.
Mr Trump told Mr Turnbull the agreement was "a terrible deal, a disgusting deal", would make him look like a "dope", "a weak and ineffective leader", and he feared the refugees would turn into terrorists who would pull off San Bernardino or World Trade Center-style terror attacks in the US.
Trump first complimented Australia's policy of refusing refugees, saying to Turnbull, "You are worse than I am".
The president went on to label the US refugee deal as "stupid" and claimed it would make him "look terrible" in his first week in the White House.
Mr Turnbull responded: "That is the point I have been trying to make".
The president complains that he "doesn't understand" why the deal is "so important" and seems to end the discussion abruptly. "I have had it".
"Turnbull asks if Trump wants to discuss Syria and North Korea; Trump replies "...this is insane". "It is an embarrassment to the United States of America and you can say it just the way I said it". "I will be there again and again".
I have had it, ' the president said. In it, the president remarks that Nieto speaks "beautifully", adding that he does not think he "can speak that beautifully".
Trump's feelings on the agreement became even more clear later on in the call.