On Wednesday, the US Navy said that recovered limpet mine fragments from one of two tanker ships that are believed to have been attacked bore a "striking resemblance" to mines seen during Iranian military parades.
In response, the U.S. military said it did not fly over Iranian airspace.
The Guard's news website, Sepah News, and Iran state news agency IRNA - which called it a "spy" drone - both reported the downing of an RQ-4 Global Hawk in the southern province of Hormozgan on Thursday.
The reported shootdown of the RQ-4 Global Hawk comes after the U.S. military alleged Iran had fired a missile at a drone last week that responded to the attack on two oil tankers near the Gulf of Oman.
RQ-4s typically fly at high altitude to conduct reconnaissance missions.
However, he told The Associated Press: "There was no drone over Iranian territory".
"No US aircraft were operating in Iranian airspace today", Navy Captain Bill Urban, a spokesman for the US military's Central Command, said.
The US has accused Iran of being behind a series of operations against oil tankers in highly sensitive Gulf waters.
Iran claims to have shot down the drone while it was over Iranian territory, however the U.S. has denied any drone was in that airspace.
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Two oil tankers were attacked on the strategic Hormuz Strait.
The attacks come against the backdrop of heightened tensions between the US and Iran following President Donald Trump's decision to withdraw from Tehran's nuclear deal a year ago.
Secretary of State Mike Pompeo has blamed Iran for the "blatant assault" on oil tankers in the Gulf of Oman.
President Trump decided a year ago to withdraw America from Iran's nuclear deal with world powers.
The incident is not the first time in recent days that Iran has targeted an American drone off its coast.
However, earlier this week, a spokesman for Iran's atomic energy agency warned that Tehran would surpass limits on its uranium stockpile under the deal and said it was prepared to increase its enrichment to a level just one step short of weapons-grade, which also violates the terms of the agreement.
On Monday, Trump ordered another 1,000 USA troops to the Middle East, which will include a Patriot missile battalion, manned and unmanned surveillance aircraft and "other deterrence capabilities", the Pentagon said. Saudi state media and officials did not immediately report a missile strike Thursday.
"We are closely monitoring the situation and continuing to consult with our partners and allies", Sanders said.
Also, Houthi rebels in Yemen on Wednesday said they hit a Saudi power station with a cruise missile.