White House Press Secretary Sean Spicer lashed out at the Obama-administration for the move, saying the new president was "unbelievably disappointed" to have inherited the deal.
Later asked if the deal would continue, Trump however said, "We'll see what happens."
Australian Prime Minister Malcom Turnbull though, had yesterday said that Trump had committed to the agreement to accept 1,250 refugees who are lodged in offshore detention centres on the Pacific nations of Nauru and Papua New Guinea.
At the event, Trump told reporters that one must respect a step taken by the previous administration, but added in the same breath that it could also be questioned.
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"A previous administration does something, you have to respect that but you could also say, why are we doing this? That's why we're in the jams that we're in," he said.
"We had one instance in Australia, I have a lot of respect for Australia, I love Australia as a country but we had a problem where for whatever reason President Obama said that they were going to take probably well over 1,000 illegal immigrants who were in prisons and they were going to bring them and take them into this country and I just said 'why?'," he said.
"We have some wonderful allies but we're going to keep it that way but we have to be treated fairly also. We have to be treated fairly," Trump said. He also lamented that a "lot of countries" were "really terribly" taking advantage of the US.
At his press conference yesterday, Spicer said Trump "had a very cordial conversation" with the Australian Prime Minister.
"The President is unbelievably disappointed in the previous administration's deal that was made and how poorly it was crafted and the threat it put on US national security," Spicer.
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"But out of respect for him, he's going to allow that process to continue to study, and allow to move forward under the conditions that have been set that there will be extreme vetting on every single one of those individuals," the White House Press Secretary said.
"But I cannot underscore how disappointed he was in the deal that was made and how he thought it was just a horrible deal that was offered up by the United States by the previous administration," Spicer said in response to a question.
Republican Senator John McCain meanwhile, said he called the Australian Ambassador to the US to calm the situation.
"I called Australia's Ambassador to the United States this morning to express my unwavering support for the US-Australia alliance. I asked Ambassador Hockey to convey to the people of Australia that their American brothers and sisters value our historic alliance, honor the sacrifice of the Australians who have served and are serving by our side, and remain committed to the safer, freer, and better world that Australia does far more than its fair share to protect and promote," McCain said.