The American warplane, identified by Iran as a F-15E Strike Eagle, was one of two attacked on Friday.
Iran has promised a reward for whoever turns in the "enemy pilot".
Iran's joint military command on Saturday said that it also struck two US Black Hawk helicopters on Friday, but The Associated Press couldn't independently verify that.
The war, now in its sixth week, began with joint US-Israel strikes on February 28 and has killed thousands, shaken global markets, cut off key shipping routes and spiked fuel prices.
It shows no signs of slowing as Iran responds with attacks across the region.
"We will continue to crush them," Israeli Prime Minister Benjamin Netanyahu said Saturday.
Israel's military confirmed that it struck a petrochemical complex in Mahshahr that Netanyahu said helps to fund the war.
Five people were killed, Iranian state media reported, citing a provincial security official.
Trump said in a national address on Wednesday that the US has "beaten and completely decimated Iran".
But on Saturday, an apparent Iranian drone damaged the headquarters of US technology company Oracle in Dubai, United Arab Emirates.
Footage verified by the AP outside the UAE showed a large hole in the building's southwestern corner.
With Iran's leadership defiant since the start of the war, its foreign minister left the door open in principle for peace talks with the US via mediation from Pakistan, but gave no sign of Tehran's willingness to bow to Trump's demands.
"We are deeply grateful to Pakistan for its efforts and have never refused to go to Islamabad. What we care about are the terms of a conclusive and lasting END to the illegal war that is imposed on us," Foreign Minister Abbas Araqchi said on X.
Trump has sent mixed messages since the conflict began, switching between hinting at diplomatic progress and making threats to bomb the Islamic Republic "back to the Stone Ages".
On Saturday, he repeated his threats to intensify attacks on Iran if it failed to reach a deal or open the key Strait of Hormuz waterway.
"Remember when I gave Iran ten days to MAKE A DEAL or OPEN UP THE HORMUZ STRAIT. Time is running out - 48 hours before all Hell will reign (sic) down on them. Glory be to GOD!" he said in a post on Truth Social.
Mediators from Pakistan, Turkey and Egypt were working to bring the US and Iran to the negotiating table, according to two regional officials.
They said that they were working on bridging the gap between the two sides' demands to stop the war and reopen the crucial Strait of Hormuz.
The proposed compromise includes a cessation of hostilities to allow a diplomatic settlement, according to a regional official involved in the efforts and a Gulf diplomat briefed on the matter.
The search for the US pilot focused on a mountainous region in Iran's southwestern province of Kohgiluyeh and Boyer-Ahmad.
More than 1900 people have been killed in Iran since the war began.
