The US drone which Iran said it had brought down penetrated 250 kilometres (150 miles) inside the Islamic republic's air space, state television's website reported on Friday.
In a letter of protest to the United Nations, the government said "the American RQ-170 spy plane violated 250 kilometres inside Iranian airspace before confronting the reaction of Iran's armed forces," the website reported.
"Provocative and secret actions by the American government against the Islamic republic in recent months" have been on the increase, it charged.
It said Tehran had lodged "a strong protest against this violation of international rules by the US government" and warned against any "repetition of such actions."
Iran called for the United Nations to condemn "this violation," in the letter addressed to the UN secretary general as well as the presidents of the Security Council and General Assembly.
State television on Thursday aired footage of what it said was the captured drone, showing what appeared to be an RQ-170 Sentinel aircraft with little visible damage.
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The Pentagon said American experts were analysing the footage.
The footage showed a cream-coloured aircraft being examined by two commanders of Tehran's elite Revolutionary Guard Corps, who are in charge of the country's air defences.
Aerospace unit Brigadier General Amir-Ali Hajizadeh said the drone had been captured through a cyber attack. "It fell into the trap of (the Guards) electronic warfare unit who then managed to land it with minimum damage," he said.
A leading conservative MP, Mohammad Kossari, on Friday delivered a stern warning of retaliation in case of further violations.
"Iran will target all US military bases around the world," said the deputy head of parliament's foreign affairs commission, quoted by Fars news agency. Its response would be "terrifying."
The RQ-170 Sentinel is a high-altitude stealth reconnaissance drone made by Lockheed Martin whose existence was exposed in 2009 by specialised reviews and later confirmed by the US Air Force in 2010.
Iranian media said on December 4 that the unmanned aerial vehicle was shot down after making an incursion into the airspace of eastern Iran, which borders Afghanistan and Pakistan.
The crash came 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.