The Pentagon and US Central Command did not respond to requests for comment.
Iranian officials called on civilians to be on the lookout for survivors and have flooded social media with images that purport to show wreckage from the aircraft.
White House Press Secretary Karoline Leavitt said Trump had been briefed, without confirming any details of the incident.
Two US officials told Reuters the aircraft was an F-15E fighter jet, which has two seats: one for a pilot and the second for a weapons systems officer.
It was unclear which of the two was recovered, and the US official who confirmed the recovery did not offer any details on how it took place.
In an email from the Pentagon obtained by the Associated Press, the US military said it received notification of "an aircraft being shot down" in the Middle East, without providing more details.
William Goodhind, a forensic imagery analyst with Contested Ground, said images of the plane's tail fin seen in photos posted on social media are consistent with that of an F-15E Strike Eagle, which carries two crew.
Alan Diehl, a former investigator for the Air Force Safety Center, said the Strike Eagle has an emergency locator beacon in a survival kit that can be set to activate automatically or manually.
The governor of Kohgiluyeh and Boyer-Ahmad province said anyone who captured or killed the crew "would be specially commended," Iranian news agency ISNA reported.
The New York Times reported that a second US Air Force combat plane
crashed in the Persian Gulf region on Friday and its only pilot was then rescued, citing two US officials.
The incident follows threats by US President Donald Trump to attack Iran's energy infrastructure and desalination plants, as he presses the country's leaders to end the war on the United States' terms.
So far, 13 US military service members have been killed in the conflict and more than 300 have been wounded, according to the US Central Command.
While Trump has repeatedly sought to portray the Iranian military as defeated, Reuters has reported on US intelligence showing Iran retains large amounts of missile and drone capability.
As of last week, the United States could only determine with certainty that it has destroyed about one-third of Iran's missile arsenal.
The status of about another third was less clear but bombings likely damaged, destroyed or buried those missiles in underground tunnels and bunkers, Reuters sources said.
The US and Israeli war with Iran has spread across the Middle East, killing thousands of people and hitting the global economy with soaring energy prices that are fuelling fears of inflation in countries around the world.
News about the downed aircraft came after Iran attacked Kuwait's Mina al-Ahmadi oil refinery.
The state-run Kuwait Petroleum Corp said firefighters were working to control several blazes.
Kuwait also said an Iranian attack caused "material damage" to a desalination plant.
Authorities in the United Arab Emirates shut down a gas field after a missile interception reportedly rained debris on it and started a fire.
Residents reported US-Israeli strikes around the Iranian capital Tehran and the central city of Isfahan on Friday but it was not immediately clear what was hit.
with AP
