"It is vitally important that this process not impact patient access to timely medical treatment."
Last Friday, Trump put a four-month hold on allowing refugees into the United States and temporarily barred travellers from Syria and six other Muslim-majority countries, saying the moves would help protect Americans from terrorist attacks.
Reuters reported earlier this week that Trump's order wreaked panic and uncertainty among refugees in the US pipeline with urgent medical needs, some of whom had prioritised applications.
The order could mean as many as 800 people needing medical entry will be denied entry, said Karen Monken of HIAS, a Maryland-based refugee assistance organisation formerly known as the Hebrew Immigrant Aid Society.
Homeland Security said in a statement the executive order "ensures a more rigorous vetting process."
"The Department of Homeland Security will continue to enforce all of President Trump's executive orders in a manner that ensures the safety and security of the American people," the agency said.
The AMA letter also pointed to the importance of international medical graduates, who comprise one out of every four physicians practising in the United States. They are more likely to work in underserved and poor communities, the group wrote, and fill training positions that face workforce shortages.
Other physician groups, including the Association of American Medical Colleges and American College of Physicians, expressed concern in separate statements earlier this week that the order would create further barriers to care.-Reuters