What caused the crash remained unclear on Tuesday in the Middle East, which was still reeling after Iran and Israel exchanged fire the previous day in the biggest strain yet to the nominal ceasefire in the Iran war.
Iranian state media, relying on foreign reporting, acknowledged the crash, without elaborating.
Since the US and Israel began striking Iran on February 28, the war has shaken the global economy, driven up energy prices around the world and made many basics, including food, more expensive.
Officials have been unable to turn the April ceasefire into a deal to permanently end the conflict.
Trump, speaking to journalists at John F Kennedy International Airport in New York after watching the NBA Finals on Monday night, acknowledged the crash.
"The pilots are fine. Yeah," Trump said.
"Nobody injured. We are going to issue a report tomorrow. But the pilots are fine."
The New York Times first reported that a US Army Apache attack helicopter went down near the strait in unclear circumstances.
The US military's Central Command and the Defense Department did not immediately respond to requests for comment from The Associated Press.
