SYDNEY, Australia — The Australian government said on Sunday that the last remaining children held on the Pacific island of Nauru while seeking asylum would be resettled in the United States, a long-awaited end to a controversial practice and a victory for migrant advocates.

“Every asylum-seeker child has now been removed from Nauru or has had their claim processed and has a clear path off the island,” Prime Minister Scott Morrison and Immigration Minister David Coleman said in a joint statement.

The move is a milestone for a coalition of lawyers, doctors and caseworkers who have pushed the government to transfer all critically ill people held in offshore detainment facilities to Australia. Currently, asylum seekers who try to reach Australia by sea are barred from settling there.

Since 2013, more than 3,000 refugees and asylum seekers have been detained on Nauru and Manus Island, which is part of Papua New Guinea. About 1,000 such migrants remain on the islands.