The leaders of Australia and Nauru have discussed the future of Canberra's detention camp on the island amid speculation the centre may close.
Canberra and Washington have a deal for some of the refugees held on Nauru to be shifted to the US while Australia takes refugees from Central America.
Nauru's president Baron Waqa said he had not sought assurances from the Trump administration that the deal would go ahead.
While the detention of asylum seekers has been a boost for Nauru's economy, reports said Australia promised not to cut and run.
Mr Waqa said maybe other countries could send their asylum seekers to Nauru for processing.
He hinted that he thought refugees on the island who are left behind might pose a risk to Nauruans.
But he played down allegations refugees and asylum seekers had been raped or physically assaulted on the island, saying the stories are often made up.
Meanwhile, the future of Australia's asylum-seeker detention centre on Manus island will be discussed during a two-day visit by Australian Prime Minister Malcolm Turnbull to Papua New Guinea starting today.
Canberra is under pressure from human rights groups and the United Nations to close its detention camps.
Last year, the PNG Supreme Court ruled that the Manus detention centre should close, forcing Australia and its Pacific Island ally to confirm it would close the camp during 2017.