The Washington Post published the full details Thursday of private calls between Trump and his Australian and Mexican counterparts, sparking fury about the leak from the US administration.
The acrimonious exchange between Trump and Malcolm Turnbull saw the American billionaire balk at a "dumb deal" made by the Obama government to accept refugees sent by Australia to remote Pacific island detention camps.
But the transcript also exposed key inconsistencies between the Australian government's comments to the public on the deal, and undermined official assertions it was not set up as a swap to take refugees from the US.
"We will take anyone that you want us to take," Turnbull told Trump during the call, adding: "The only people that we do not take are people who come by boat.
"We would rather take a not very attractive guy that helps you out than to take a Nobel Peace Prize winner that comes by boat."
Turnbull today described the call as "frank and courteous" and defended what he told Trump, telling reporters "the nature of our relationship with the United States in this area is one of mutual assistance.
"So we help the Americans, they help us," he said.
He also played down his remarks that the Americans could take as few refugees as they wanted, even though the deal was meant to help transfer hundreds off Manus island in Papua New Guinea before the closure of the camp there in October.
A PNG Supreme Court ruling declaring that holding people on Manus was unconstitutional has meant Canberra is keen to remove the refugees ahead of it shutting.
Australia sends asylum-seekers who try to enter the country by boat to camps on Nauru and Manus, with even those found to be refugees barred from resettling in Australia.
The widely-criticised policy was adopted following a sharp upsurge in the number of asylum-seekers arriving by boat. Canberra defends its position, which includes turning boats back, saying it has prevented deaths at sea.
"It does not oblige you to take one person that you do not want," Turnbull told Trump during the call, in remarks criticised by refugee advocates as the Australian leader going through the motions.
Turnbull said today the deal "has always been subject to American vetting procedures, that's always been part of the arrangement".
The Human Rights Law Centre said it showed Turnbull was "totally preoccupied with maintaining (its) facade".
"The conversation makes it clear that Prime Minister Turnbull is rolling the dice with people's lives and mental health," Amnesty International added.
Trump after the phone call grudgingly agreed to honour what he has called a "dumb deal", although it remains unclear how many Washington will accept.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)