The 9th US Circuit Court of Appeals ruling came in a challenge to Mr Trump's order filed by the states of Washington and Minnesota. The US Supreme Court will likely determine the case's final outcome.
An executive order by Mr Trump temporarily banned entry for all refugees and visitors from seven mainly Muslim countries.
Federal judge James Robart, responding to a challenge by Washington state, suspended the order last Friday.
The 9th US Circuit Court of Appeals in San Francisco heard arguments earlier this week from Justice Department lawyers and opposing attorneys.
Mr Trump's executive order, signed on 27 January, imposed a 120-day halt on refugees entering the US and barred citizens from Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen for 90 days.
It sparked protests and chaos at US and overseas airports in the weekend that followed.
Photo: AFP Donald Trump