Donald Trump has strongly criticised a deal that would allow mostly Muslim refugees rejected by Australia to move to the US.
He called the agreement "dumb" and vowed to review it, although Australia's prime minister insisted that it was still on.
Barack Obama had agreed the deal to resettle refugees from among around 1,600 asylum seekers, most of whom are on island camps on the Pacific nations of Nauru and Papua New Guinea.
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!"
It came hours after The Washington Post published a story detailing a tense exchange between Mr Trump and Prime Minister Malcolm Turnbull during their first telephone call as national leaders.
The newspaper reported that during the call, an angry Mr Trump dubbed the agreement "the worst deal ever".
It said he accused Mr Turnbull of seeking to export the "next Boston bombers" - a reference to Tamerlan and Dzhokhar Tsarnaev, US citizens born in Kyrgyzstan, who set off two bombs at the 2013 Boston marathon.
Mr Turnbull declined to comment on the report, which also said Mr Trump abruptly ended the expected hour-long conversation after 25 minutes.
"It's better that these things - these conversations - are conducted candidly, frankly, privately," the PM said.
Later, however, he denied that Mr Trump had hung up on him, saying the conversation had ended "courteously".
Mr Turnbull said the strength of the relationship between the two nations was evident in that Mr Trump had agreed to honour the deal.
Australia has refused to accept the asylum seekers and instead pays for them to be housed on the impoverished islands.
"I can assure you the relationship is very strong," Mr Turnbull said.
"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."
Mr Trump, a day before the conversation with Mr Turnbull, had signed an executive order suspending the admission of refugees.
The president complained during the call that he was "going to get killed" politically by the deal, the Post reported.
"I don't want these people," Mr Trump reportedly said.
He also told Mr Turnbull he had spoken to four world leaders that day and "this is the worst call by far".
Mr Trump told Mr Turnbull that it was "my intention" to honour the agreement, a phrase designed to leave the president wriggle room to back out of the deal, the newspaper reported.
There have been mixed messages from Washington all week on the state of the agreement.
White House spokesman Sean Spicer confirmed on Wednesday that Mr Trump had agreed to honour the deal.
But the White House said on Thursday: "The president is still considering whether or not he will move forward with this deal at this time."
Yet the US State Department said later in the day the United States would honour the agreement "out of respect for close ties to our Australian ally and friend".
In an earlier phone call with his Mexican counterpart, Mr Trump reportedly warned he was ready to send US troops to stop "bad hombres down there" unless the Mexican military does more to control them.
The comment was in an excerpt of a transcript of the conversation with Enrique Pena Nieto on Friday obtained by The Associated Press.
Mr Trump said: "You have a bunch of bad hombres down there. You aren't doing enough to stop them. I think your military is scared. Our military isn't, so I just might send them down to take care of it."
The president also turned his attention to Iran, tweeting: "Iran is rapidly taking over more and more of Iraq even after the U.S. has squandered three trillion dollars there. Obvious long ago!"
That came after the White House issued a warning that the US will act against Iran unless it stops testing ballistic missiles and supporting Houthi rebels in Yemen.
Michael Flynn, Mr Trump's national security adviser, forcefully denounced Iran's behaviour.
"As of today, we are officially putting Iran on notice," he said.