Iranian and American forces were racing each other early Saturday to recover a crew member of the first US fighter jet to go down inside Iran since the start of the war.

Tehran said it had shot down the F-15 warplane, while US media reported American special forces had rescued one of its two crew members, with the other still missing.

Iran's military also said it downed a US A-10 ground attack aircraft in the Gulf, with US media saying the pilot was rescued.

The war erupted more than a month ago with US-Israeli strikes on Iran that killed supreme leader Ali Khamenei, triggering retaliation that spread the conflict throughout the Middle East, convulsing the global economy and impacting millions of people worldwide.

US Central Command did not immediately respond to a request for comment on the loss of the F-15, but White House Press Secretary Karoline Leavitt said: "The president has been briefed".

President Donald Trump told NBC the F-15 loss would not affect negotiations with Iran, saying: "No, not at all. No, it's war."