Tehran insists that the drone violated its airspace - something Washington denies - but was prepared to accept on Friday that it might have done so by accident.
Washington and its allies will pay dearly for any act of aggression against Tehran, an Iranian general has said, vowing to retaliate with overwhelming force if the USA dares to fire even "one bullet" at the Islamic Republic.
Over the past month, Iran has also been blamed for a series of attacks on oil tankers in the Gulf.
The statement said he was executed in the Rajai-shahr Prison but didn't say when.
The intruding drone was reportedly shot by Iran's homegrown air defense missile system "Khordad-3rd".
The strongly-worded response from Iran comes just a day after the USA military was all set to retaliate in response to the downing of its BAMS-D RQ-4A Global Hawk High-Altitude Long Endurance (HALE) Unmanned Aircraft System (UAS) by the former's armed forces.
The move "proved that Iran will not surrender easily to their (Americans') nonsensical talks", Pezeshkian, a reformist, said at the beginning of an open session of the parliament on Sunday.
Under pressure to respond to the high-stakes incident near the strategic Strait of Hormuz, Trump said the USA was prepared to hit "3 different sites" Thursday night but that he scrapped the strikes "10 minutes" before they were to have been launched.
Washington said the incident had occurred in global airspace.
Worries about a confrontation between Iran and the United States have increased despite Mr Trump saying that he has no appetite to go to war with Iran.
The incident happened amid a volatile situation between Washington and Tehran as the Trump administration warned industry officials to be alert for cyber attacks originating from Iran.