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.
