SYDNEY, Australia — The Australian government said Sunday that it had reached a one-time agreement in which the United States would take in refugees who had been banished to a detention center on the tiny impoverished Pacific island nation of Nauru.

Prime Minister Malcolm Turnbull and the immigration minister, Peter Dutton, said the government would first resettle refugee women, children and families.

Refugees held at another offshore processing center, Manus Island, a province of Papua New Guinea, may also be considered for resettlement in the United States. Asylum seekers who have not been granted refugee status should return home, Mr. Turnbull said.

Mr. Turnbull would not say how many of the refugees, who were granted that status by the United Nations, would be resettled in the United States. “U.S. authorities will conduct their own assessment of refugees and decide which people are resettled in the U.S.,” he said in a written statement. About 410 men, women and children are held on Nauru, and 823 men are held on Manus Island. Some are from Iran, Afghanistan, Vietnam and Malaysia.