The Washington Post reported that Trump called the conversation with Turnbull "the worst by far" of his calls with world leaders that day, and cut it short after 25 minutes.
During Trump's call with Turnbull last Saturday, the US President objected to an agreement over America receiving refugees, the CNN reported.
The disagreement came as the two leaders discussed an agreement, reached under the Obama administration, for the US to accept over 1,200 refugees from Australia who are living on islands in detention centers off the mainland due to strict government policies.
US media reports say Trump insisted it was a very bad deal for the US to take 2,000 refugees and that one of them was going to be the "next Boston bomber".
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Turnbull told Trump several times the agreement was for 1,250 refugees, not 2,000.
Trump expressed concern as to how this agreement from President Barack Obama's administration would go forward given his executive order the day before temporarily suspending the US refugee programme.
Later, Trump tweeted, "Do you believe it? The Obama Administration agreed to take thousands of illegal immigrants from Australia. Why? I will study this dumb deal!"
In Canberra, Turnbull attempted to keep some semblance of diplomacy, declining to elaborate on details of the call.
"Look, I'm not going to comment on a conversation between myself and the President of the United States other than what we have said publicly, and you can surely understand the reasons for that," he said. "I'm sure you can understand that. It's better these conversations are conducted candidly, frankly, privately. If you'll see reports of them, I'm not going to add to them."
Leading Australian newspaper, The Sydney Morning Herald commented that Trump's behaviour "came as a shock for many in Australia and overseas that Mr Trump would publicly create waves with such a strong ally."
"However, the tweet follows Mr Trump's established behaviour on social media since he was elected," it said.