A projectile hit near Iran’s Bushehr nuclear plant, killing a worker.

President Trump and Defense Secretary Pete Hegseth have boasted in recent days that U.S. and Israeli strikes have decimated the Iranian regime and military. Mr. Hegseth said earlier this week that the United States had achieved such control of Iran’s skies that it was flying B-52 bombers directly over Iranian territory for the first time since the war began.

But the downing of the F-15E and the damage to the A-10 underscores how a weakened Iranian military can still fight back with a limited but still lethal arsenal of missiles and drones.

The loss of the F-15E Strike Eagle is the first known instance of an American combat aircraft going down in hostile territory in the monthlong U.S.-Israeli war in Iran. Three Air Force F-15Es were shot down by friendly fire over Kuwait on March 2, and all six crew members in that episode ejected safely.

The U.S. military’s Central Command keeps multiple task forces set up near Iran for search and rescue operations in the event that American warplanes are shot down, including in both Iraq and Syria, the officials said, speaking on the condition of anonymity to share operational details.

But such an operation is extremely dangerous because Iran still retains antiaircraft weapons and, without the support of U.S. troops on the ground, the loss of recovery aircraft to hostile fire can turn an already difficult situation into a catastrophe.

On Friday, a U.S. UH-60 Black Hawk helicopter involved in the rescue efforts for the F-15E was hit by ground fire but was able to keep flying and escaped safely, U.S. and Israeli officials said.

Open source images show U.S. military aircraft, primarily transport helicopters and cargo planes, over Iran. U.S. forces would not launch this type of a mission without verified crew contact or an active ejection seat beacon, a U.S. fighter pilot said. The pilot spoke on the condition of anonymity to describe current military operations.

Rescue operations are also inherently dangerous because additional American service members are put at risk over hostile territory. In June 2005, a rescue mission that was part of an operation called Red Wings went horribly wrong. Rescuers were sent after a team of four U.S. Navy SEALs who had been ambushed by Taliban forces in eastern Afghanistan. A rescue helicopter was shot down, killing 16 service members.

In an address to the nation on Wednesday night, Mr. Trump said the United States was on track to complete its military objectives in Iran soon.

“Over the next two to three weeks, we’re going to bring them back to the Stone Ages, where they belong,” the president said, promising intense bombing.

Mr. Hegseth quickly repeated his boss’s words on social media.

“Back to the Stone Age,” Mr. Hegseth wrote.

The F-15’s ability to fly long distances and carry a large amount of munitions has made it essential for the U.S. air war over Iran. The F-15 can carry up to 24,500 pounds of ordnance but it typically flies with about 10,000 pounds of munitions, according to military documents.

American combat aircraft losses have been relatively light since the Iran war started on Feb. 28. In addition to the three F-15Es shot down by friendly fire, a KC-135 tanker crashed in western Iraq after an apparent midair collision with another tanker, resulting in the deaths of six airmen.

By comparison, the United States lost 42 combat aircraft in the 43-day air campaign of the 1991 Persian Gulf war, according to David A. Deptula, a retired three-star Air Force general who was a main architect of the operation, Desert Storm.

In his first remarks since the fighter was shot down, Mr. Trump declined to comment to NBC News about the search and rescue mission. But he said the incident would not affect negotiations over a cease-fire with Iran.

The search for the downed crew in Iran is among the most intense American military rescue operations since two missions during the Balkans wars in the late 1990s.

In March 1999, an F-117A stealth fighter, the premier attack plane in America’s arsenal at the time, was shot down over the former Yugoslavia. Hours later, helicopters swooped in to snatch up the pilot after he had signaled his rescuers with an emergency beacon.

Nearly four years earlier, in June 1995, Capt. Scott F. O’Grady’s Air Force F-16 fighter jet was shot down by a SA-6 missile over Bosnia. Captain O’Grady evaded capture for six days, scrounging for water and digging for ants to eat, before he was rescued.

Yeganeh Torbati contributed reporting from Istanbul. Tyler Pager contributed reporting from Washington.