Nauru's president Baron Waqa says he's confident refugees housed on the island by Australia will eventually find a nation to take them.
United States officials have been assessing refugees on Nauru and Manus Island in Papua New Guinea for a swap deal between US and Australia.
The scheme was agreed to last year by President Obama. President Trump has criticised it although says he will allow it.
The deal would see some refugees moving to the US and Australia taking some Central American refugees from the US.
President Waqa said if the deal falls over the process will continue.
He said the US solution is not the only solution.
The swap was designed, in part, to help Australia close both Manus and Nauru offshore centres, which are expensive to run and have been widely criticised by the United Nations and others over the treatment of detainees.
The US government said its cap of 50,000 refugees had been reached for the year and a new intake year was not due to begin until 1 October.