But Mr. Turnbull denied that, saying that "the president assured me he would follow through" on the deal.
At one point Trump informed Turnbull that he had spoken with four other world leaders that day - including Russian President Vladimir Putin - and that, "This was the worst call by far". Trump also reportedly bragged to Turnbull about the size of his Electoral College victory.
Senior U.S. officials told The Washington Post that Trump berated Turnbull over an agreement struck during the Obama administration that would ask the U.S.to accept 1,250 refugees from an Australian detention center.
Trump told Turnbull he had spoken to four other global leaders that day, including Russian President Vladimir Putin, and "this was the worst call by far", the paper reported, citing unidentified U.S. officials. President Trump then terminated the call after a mere 25 minutes even though it had been scheduled for an hour, the Post stated.
The phone call between Trump and Turnbull was one of four the USA president had with world leaders, including Russia's Vladimir Putin last Saturday. White House sources say the president will impose new sanctions against Iran.
Mr Trump called the exchange "very civil" in a tweet, adding that "fake news" media had lied about the exchange.
Pressed on the issue at a press conference today, Mr Turnbull declined to reveal any of the details of his conversation with Mr Trump.
"Australia is one of America's oldest friends and staunchest allies", the Arizona Republican said in a statement.
The phone call with Turnbull occurred a day after Trump signed a controversial executive order suspending refugee admissions.
The United States also plans to send extra military aircraft to Australia's tropical north this year as part of a US Marines deployment to bolster its military presence close to the disputed South China Sea.
That came after the White House issued a warning that the USA will act against Iran unless it stops testing ballistic missiles and supporting Houthi rebels in Yemen.
The characterizations in the Washington Post's report are unsurprisingly at odds with the version released by the White House.