The NATO-led military force in Afghanistan said the drone reportedly shot down by Iran "may" belong to the United States.
"The UAV (unmanned aerial vehicle) to which the Iranians are referring may be a US unarmed reconnaissance aircraft that had been flying a mission over western Afghanistan late last week," the International Security Assistance Force (ISAF) said.
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"The operators of the UAV lost control of the aircraft and had been working to determine its status," the statement said without elaborating on the type of drone.
Iran's Al-Alam Arabic language satellite channel, quoting a military source in Iran's joint chiefs of staff, said late Sunday that a RQ-170 unmanned aerial vehicle was shot down "a few hours ago."
The Fars news agency, which has close ties to the Revolutionary Guards responsible for Iran's air defence and ballistic missile systems, said the drone had made an incursion into Iran's eastern airspace.
"Our air defence and electronic warfare units managed to identify and shoot down an advanced unmanned spy aircraft -- an RQ-170 -- after it briefly violated the eastern border territory," Fars said.
Quoting an unnamed military source, Fars said the drone "was downed with slight damage."
"It is now under the control of our forces."
The source warned that Iran's armed response would "not be limited to our country's borders" for the "blatant territorial violation."
No images of the drone said to have been shot down were immediately published by any of the media carrying the reports.
The RQ-170 Sentinel is a high-altitude reconnaissance drone whose existence was revealed in 2009 by specialised reviews and later confirmed by the US Air Force in 2010.
In January, Iran announced that its forces had downed two US drones after they violated Iranian-controlled airspace.
It said it would put the aircraft on display to the public, but there has been no indication it ever did so.
In June, Brigadier General Amir-Ali Hajizadeh, the commander of the Guards' aerospace unit, said Iran had shown Russian experts the US drones in its possession.
"Russian experts requested to see these drones and they looked at both the downed drones and the models made by the Guards through reverse engineering," he said.
Hajizadeh did not specify how many US drones were shown nor give any details of the copies Iran was said to have made of the aircraft.
The US military and the CIA routinely use drones to monitor military activity in the region.
They have also reportedly used them to launch missile strikes in Yemen as well as in Afghanistan and in Pakistan's lawless tribal belt.
The latest report comes as relations between Pakistan and the US have hit a new low after 24 Pakistani soldiers were killed in an air strike near the Afghan-Pakistani border last month, prompting Pakistan to boycott Monday's Bonn conference on Afghanistan's future.
It also comes at a time of heightened political tension over Iran's nuclear programme, with speculation rife that Israel is mulling air strikes against Iranian atomic facilities, with or without US backing.
Iranian officials and Guards commanders, who regularly boast about Tehran's military capabilities, have warned against any such military action targeting the Islamic republic.
