Despite the "frank and forthright" nature of the call, Turnbull said "I have made the case as powerfully and persuasively as I can with the Trump administration".
Following an awkward press conference where Turnbull refused to comment about the discussion, the US Embassy in Australia released a statement that the deal would go ahead.
A day of intense confusion has reigned despite the Prime Minister confirming with Sydney radio station 2GB "the report the President hung up is not correct".
While this was happening, Americans took to social media to express their support for one of their country's biggest allies.
Despite Australia being one of America's "staunchest allies", White House bureau chief at the Washington Post Philip Rucker told the ABC that Trump "doesn't really care so much that Australia is an ally over many, many years".
"The thing you have to understand about Donald Trump is that he is not a natural diplomat, he is not a politician," he said in an interview.
"He has a career in real estate, in business and deal-making, and he ran for President as somebody who was going to disrupt the world order.
"He was going to make changes and he was going to blow up the system -- literally -- and disrupt what he sees as a world order that is failing the world and making it more dangerous and less safe.
"And so he doesn't really care so much that Australia is an ally over many, many years. What he cares about is the refugee policy that he views as dangerous for the United States. So he didn't let diplomatic niceties get in the way of how he felt about that refugee policy."
It comes as CNN's senior White House correspondent Jim Acosta tweeted that a source from inside Trump's camp said the President's conversations "are turning faces 'white' inside the White House".
Acosta also tweeted that during his call with Turnbull, President Trump "pulled phone away from ear and says he wants off call".
The call then ended abruptly, according to the source.
Rucker said he was unclear over what the PM said in response to Trump.
He said Trump has left himself "a little bit of wriggle room to get out of that deal if he so chooses down the road, but nevertheless he gave the Prime Minister his assurances that he intended to stick with the deal".
Yet Rucker said he and his Washington Post colleague, Greg Miller, heard about the conversation through "senior US officials who have been briefed on some of the exact quotations from the conversation".
The officials "shared that information with us".
Rucker described the call as "pretty extraordinary", saying the tone and substance of it certainly differs from the relatively sanitised account that came out of both governments on Saturday.
The US President reportedly blasted Turnbull during their conversation on Saturday, saying "this was the worst call by far".
Trump was apparently angry about having to honour the refugee deal with Australia and blew up at Turnbull over the agreement, which will give US entry to 1250 refugees from Naura and Manus Island.
"Trump objected to that," Rucker said.
"He feels like that that's a bad deal. He thinks it hurts him politically at home in the United States, and he feels like, I think, most importantly, that this would be a threat to national security and he told the Prime Minister as much.
"He said he thought Australia might be trying to export 'the next Boston bomber', and that is a reference of course to the Boston Marathon terrorist attack a few years ago.
According to the Washington Post, what should have been a pleasant hour-long call was ended after 25 minutes when Trump abruptly hung up on the PM.
"This is the worst deal ever," Trump reportedly said about the refugee deal, complaining that he was "going to get killed" politically.
In a conversation that was characterised as "hostile and charged" and which contrasted with productive talks held with other countries, Trump apparently told the PM he had spoken with four other world leaders that day, including Russian President Vladimir Putin, and "this was the worst call by far".
