A channel affiliated with Iranian state television claimed that a US fighter pilot ejected from their aircraft over south-western Iran.
It was not clear what may have happened to the plane on Friday, including whether Iran was claiming it was shot down or there was another issue.
If the claim is confirmed, it could lead to yet another dramatic escalation in the war, nearing the end of its fifth week.
The US did not respond immediately to requests for comment.
The anchor on the Iranian channel urged residents to hand over any “enemy pilot” to police and promised a reward for anyone who did.
The channel is in Kohkilouyeh and Boyer-Ahmad province, an intensely rural and mountainous region that spans over 15,500 square kilometres (5,900 square miles).
An on-screen crawl earlier urged the public to “shoot them if you see them,” referring to social media footage circulating of what appeared to be US aircraft in the area.
The channel showed metal debris in the back of a pickup truck while making the announcement but provided no other immediate details.
Throughout the war, Iran has made a series of claims about shooting down piloted enemy aircraft that turned out not to be true.
Friday was the first time that Iran went on television urging the public to look for a suspected downed pilot.
US Central Command, the Pentagon and the White House did not immediately respond to requests for comment.
The claim came as Iran fired on targets across the region, setting Kuwait’s Mina al-Ahmadi oil refinery one fire.
The state-run Kuwait Petroleum Corp said firefighters were working to control several blazes there.
Kuwait also said that an Iranian attack caused “material damage” to a desalination plant.
Such plants are responsible for most of the drinking water for Gulf states, and they have become a major target in the war.
Tehran has kept the pressure on Israel and its Gulf Arab neighbours, despite US and Israeli insistence that Iran’s military capabilities have been all but destroyed.
Iran’s attacks on Gulf energy infrastructure and its tight grip on the Strait of Hormuz, through which a fifth of the world’s oil and natural gas transits in peacetime, have roiled stock markets, sent oil prices skyrocketing, and threatened to raise the cost of many basic goods, including food.
Spot prices of Brent crude, the international standard, were around 109 dollars (£82.52) on Friday, up more than 50% since the start of the war, when Iran began restricting traffic through the Strait of Hormuz.