"It was shot down when it entered Iran's airspace near the Kouhmobarak district in the south," the Guards' website added
Iran's elite Revolutionary Guards have shot down a US "spy" drone in the southern province of Hormozgan, which is on the Gulf, the Guards' news website Sepah News said on Thursday.
State news agency IRNA carried the same report, identifying the drone as an RQ-4 Global Hawk.
"It was shot down when it entered Iran's airspace near the Kouhmobarak district in the south," the Guards' website added.
The RQ-4 Global Hawk unmanned aircraft system (UAS) can fly at high altitudes for more than 30 hours, gathering near-real-time, high-resolution imagery of large areas of land in all types of weather, maker Northrop Grumman says on its website.
A spokesman for the US military's Central Command said no US aircraft were flying over Iran on Wednesday.
"No US aircraft were operating in Iranian airspace today," the spokesman, Navy Captain Bill Urban, said shortly before midnight.
Urban declined further comment. The US military has in recent days confirmed an attempt by Iran to shoot down a US drone last week as well as the successful shooting down of one on June 6 by Iran-aligned Houthi forces in Yemen.
A senior Iranian security official said on Wednesday Iran would "strongly respond" to any violation of its airspace.
"Our airspace is our red line and Iran has always responded and will continue to respond strongly to any country that violates our airspace," the semi-official Tasnim news agency quoted the secretary of Iran's Supreme National Security council as saying.
Tension between Iran and the United States has spiked since last year when President Donald Trump withdrew from a 2015 nuclear deal between Iran and major powers and reimposed sanctions on it.
Concern about a military confrontation has increased since attacks on two oil tankers in the Gulf of Oman last week and on four tankers off the United Arab Emirates on May 12, both near the Strait of Hormuz, a major conduit for global oil supplies.
The United States and its regional ally, Saudi Arabia, blamed Iran for the incidents. Iran has denied responsibility.
The US military has sent forces, including aircraft carriers, B-52 bombers and troops to the Middle East. However, Trump said he does not seek war with Iran.
Iran said last week that it was responsible for the security of the Strait of Hormuz, calling on American forces to leave the Gulf.
In protest at Trump's "maximum pressure", in May Iran said it would start enriching uranium at a higher level unless other European signatories to the nuclear deal protected its economy from the US sanctions within 60 days.