While Trump has said he would honour the agreement, concerns remain about how many asylum-seekers will be resettled from the Australian-run centres.
Australian Prime Minister Malcolm Turnbull said on Wednesday the first group of about 50 men and woman held in two controversial detention centres for asylum-seekers on remote Pacific islands will be resettled in the United States within weeks.
Turnbull's comments mark the first official timetable for when the United States would begin resettling up to 1,250 people held in Australian-run centres on Nauru and Papua New Guinea's Manus island as part of a refugee swap deal struck by former U.S. President Barack Obama late last year.
Australia will begin resettling several dozen Central American refugees within weeks as part of a deal that U.S. President Donald Trump has described as "dumb" but has nevertheless said Washington would honour.
"There will be about 25 from both Manus and Nauru will be going to the United States and I just want to thank again President Trump for continuing with that arrangement," Turnbull told Australia's Seven Network.
Three sources familiar with the process said approximately 25 men from countries such as Bangladesh, Iran, and Rohingya Muslims from Myanmar held on Manus island would be the first to be informed on Wednesday. A similar number held on Nauru would be told on Thursday, they said.
Nearly 2,000 men, women and children are held on Manus island and Nauru, the majority of whom have been awarded refugee status by the two tiny Pacific countries.
Despite their refugee status, many have been held for four years in conditions widely criticised by the United Nations and human rights groups.
Australia is under increased pressure to resettle asylum-seekers from Manus Island because the centre there is due to close on Oct. 31.
Australia would need to make alternative arrangements should the bulk of the 800 men still be there by that deadline.
Under Canberra's hardline immigration policy, asylum-seekers intercepted at sea trying to reach Australia are sent for processing at the Manus island and Nauru camps. They are told they will never be settled in Australia.
Australia said last week approximately 200 men who have had their refugee applications denied and have therefore been ruled ineligible for resettlement in the United States, and who are from countries such as Iran that do not allow forced deportations, will be transferred to a new detention facility on PNG after Oct. 31.
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