A US fighter jet has been shot down over Iran and a search-and-rescue operation is underway for any survivors, two US officials told the Reuters news agency on Friday, in the first such known incident since the conflict began nearly five weeks ago.

One crew member was rescued, according to Israeli media citing Israeli officials, and CBS News citing US officials. 

The Pentagon and US Central Command did not respond to requests for comment.

The prospect of US pilots being alive and on the run inside Iran raises the stakes for the United States in a conflict that has struggled to win popular support among Americans, according to opinion polls.

It also presents a challenge to the US military, which faces the twin goals of trying to save the lives of any surviving US crew and safeguarding whoever is involved in perilous rescue missions.

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.

The governor of Kohgiluyeh and Boyer-Ahmad province said anyone who captured or killed the crew "would be specially commended," Iran's semi-official news agency ISNA reported.

The incident follows threats by US President Donald Trump to bomb the country back to the "Stone Age," including to attack Iran's energy infrastructure and desalination plants, as he presses Tehran to end the war on US 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. No US troops have been taken prisoner by Iran.

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 a third of Iran's missile arsenal. The status of around another third was less clear but bombings likely damaged, destroyed or buried those missiles in underground tunnels and bunkers, sources said.