The deal — which involves resettling in the U.S. an undisclosed number of asylum seekers being held in Australian processing centers on Nauru and Manus — was a topic of conversation between Trump and Australian Prime Minister Malcolm Turnbull during a 25-minute phone call they had on Saturday, according to Turnbull.
While Turnbull acknowledged that he and Trump discussed the deal, the White House readout of the call made no mention of it. It merely stated, "Both leaders emphasized the enduring strength and closeness of the U.S.-Australia relationship that is critical for peace, stability and prosperity in the Asia-Pacific region and globally."
ABC News has asked White House officials for further details about the phone call, but they have yet to comment.
Meanwhile, Sen. John McCain, R-Ariz., said in a statement that he spoke Thursday morning with Australia's ambassador to the U.S., Joe Hockey, to express his "unwavering support" for the U.S.-Australia alliance.
"Australia is one of America’s oldest friends and staunchest allies," McCain said. "We are united by ties of family and friendship, mutual interests and common values and shared sacrifice in wartime. 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."
"The president has committed to honor the existing arrangement, but the screening processes ... are very thorough and take some time," Turnbull said.
Peter Dutton, Australia's minister for immigration and border protection, echoed Turnbull's sentiments. "So there have been people, obviously U.S. officials, up on Nauru, and there have been conversations, exchange of information otherwise, between those officials and officials within my department," Dutton said. "So that will take some time, because obviously the U.S., rightly under the existing arrangement — both signed off on by President Obama and now adopted by President Trump — under that arrangement there is the ability for the U.S. to conduct those rigorous tests and then ultimately to have the final say, as is obviously appropriately the case, as to who will eventually end up in the U.S."
At the press conference, Turnbull said, "Our commitment to multiculturalism, our commitment to a nondiscriminatory immigration program is well known."
ABC News' Devin Dwyer contributed to this report.