The apparent disagreement was over an exchange of refugees agreed between Australia and the Obama administration late last year.
On Twitter, the US President said he would “study this dumb deal”.
Under the terms, the US would re-settle up to 1,250 asylum seekers, most of whom are held in processing camps on the Pacific islands of Nauru and Papua New Guinea.
In return, Australia would take refugees from El Salvador, Guatemala and Honduras.
But during Mr Trump’s weekend conversation with Australian Prime Minister Malcolm Turnbull, the US President is reported to have described the refugee agreement as “the worst deal ever”.
According to The Washington Post, he also accused Mr Turnbull of trying to export the “next Boston bombers”, referring to Tamerlan and Dhozkar Tsarnaev, Russia-born US citizens who set off two bombs at the 2013 Boston marathon.
Three people were killed in the blast and more than 260 injured.
Mr Trump reportedly told Mr Turnbull: “I don’t want these people.”
He is also reported to have said that he had spoken to four world leaders that day and “this is the worst call by far”.
He is reported to have told Mr Turnbull that it was “my intention” to honour the deal, words that would leave him room to back out.
Do you believe it? The Obama Administration agreed to take thousands of illegal immigrants from Australia. Why? I will study this dumb deal!
— Donald J. Trump (@realDonaldTrump) February 2, 2017
About 25 minutes into the call, which had been expected to last an hour, Mr Turnbull reportedly tried to steer on to other topics, such as Syria.
But Mr Trump had had enough and, despite Australia being one of the US’ staunchest allies, he cut their conversation short, the Post said.
Speaking at the National Prayer Breakfast on Thursday, Mr Trump said he would no longer put up with other nations taking advantage of the US.
He said: “When you hear about the tough phone calls I’m having, don’t worry about, just don’t worry about it, they’re tough, we have to be tough, it’s time we have to be a little bit tough folks.
“We’re taken advantage of by every nation in the world virtually, it’s not going to happen anymore.”
Mr Turnbull would not confirm the reports, saying: “It’s better that these things – these conversations – are conducted candidly, frankly, privately.”
The Australian leader told reporters: “The fact we received the assurance that we did, the fact that it was confirmed, the very extensive engagement we have with the new administration underlines the closeness of the alliance.”
There are also mixed messages coming from Washington DC.
White House spokesman Sean Spicer said on Wednesday that Mr Trump had agreed to honour the deal but a White House statement sent to the Australian Broadcasting Corporation on Thursday said Mr Trump was “still considering whether or not he will move forward with this deal at this time”.
The State Department also said the US would honour the agreement “out of respect for close ties to our Australian ally and friend”.
But Mr 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.”