The Christian children's charity had urged the Australian government "to seal the deal" with Donald Trump over the future of refugees being housed by Australia on the Pacific island nations of Nauru and Papua New Guinea.
Chief advocate, Rev Tim Costello, said: "No group of refugees in the world have had their refugee applications more thoroughly reviewed than those who have been held in indefinite detention on Manus Island and Nauru.
"They are being held in limbo only because the Australian Government refuses to accept asylum-seekers who attempted to reach Australia by boat, not because they are not genuine refugees."
Struck by Barack Obama, the agreement committed the United States to resettle the refugees among 1,600 asylum seekers, predominantly living in Nauru and Papua New Guinea.
But writing on Twitter following a conversation with the Australian prime minister, Mr Trump said: "Do you believe it? The Obama Administration agreed to take thousands of illegal immigrants from Australia. Why? I will study this dumb deal!"
He posted on social media hours after the Washington Post revealed details of the tense telephone exchange during which the president allegedly accused Australian PM Malcolm Turnbull of trying to export terrorists.
World Vision Australia is also urging the Australian government to "reveal its plans for asylum seekers not accepted by the US" from Nauru and Papua New Guinea.