Prime Minister Scott Morrison says the final four asylum-seeker children in the Australian-run camps on Nauru had all had their claims to be resettled in the United States processed.
Australia's right-leaning government has repeatedly defended its policy of detaining migrants at offshore facilities.
This year's annual Pacific summit, which wraps up in Nauru on Thursday, has been one of the most contentious in the event's 49-year history.
The diplomatic spat pits Nauru against the Asian superpower.
Nauru is hosting leaders of 18 Pacific nations, plus delegations from the United States and China, at a time of growing tension and rivalry in a strategically important region with access to swathes of resource-rich ocean.
Nauru's government harbours a deep mistrust of the media and is limiting reporting opportunities at this year's Pacific Islands Forum (PIF) summit, which it will host.
People-smugglers are an evil scourge taking money from men, women and children - they don't care whether they make Australian land or go to the bottom of the ocean.
The asylum-seekers held in Australian-run detention centres in the Pacific are likely to remain there indefinitely as no other country is willing to resettle them.
US officials halted screening interviews and departed the Pacific island of Nauru on Friday, two weeks short of their scheduled timetable and a day after Washington said the United States had reached its annual refugee intake cap.
Detainees said interview dates on their applications were removed on Saturday, hours after Trump signed his executive order.
Amnesty, which said its findings were based on both desk research and field work in Nauru between July and October, said the detention was a "systematic regime of neglect and cruelty."
Hitting back at the claims contained in the leaked documents, which date from 2013 to 2015, the Nauruan government said asylum-seekers had made up most of them in hope of being relocated to Australia.
In the latest criticism of the Canberra's controversial stance, Amnesty and HRW said asylum-seekers and refugees on Nauru suffered "severe abuse, inhumane treatment, and neglect".
Turnbull has warned against being "misty-eyed" over immigration and Australian Immigration Minister Peter Dutton reiterated on Friday there would be no policy change.