The group, al-Bonyan al-Marsous, quoted an IS militant who witnessed the attack as saying all but one of the 21 showed no resistance to their impending decapitation.
The militant, arrested last year, said filming the beheadings was disrupted when one of the Christians resisted. He was beaten into submission.
A grisly video of the beheadings was posted online in February 2015, shocking Egyptians and prompting the Cairo government to stage punitive airstrikes against militant targets in Libya.
They were made to kneel before they were simultaneously beheaded. The video makers identified themselves then as IS' Tripoli Province.
One militant, dressed differently than the others, spoke to the camera in North American-accented English, promising more attacks on Christian Copts, who account for roughly 10 per cent of Egypt's 95 million people.
Egypt has since December seen a series of IS attacks that have killed nearly a 100 Christians.
The filming of the video, today's al-Bonyan al-Marsous statement said, was halted again for the speaker to receive instructions. The unnamed militant said he was in charge of ferrying the bodies in his truck to bury them south of Sirte.
The bodies of the 21 Copts, with hands cuffed behind their backs, were recovered yesterday. Preparations were underway to hand over the bodies to their families, said the statement.
Libya's Chief Prosecutor Al-Sadiq al-Sour said last month that more than 800 arrest warrants have been issued to hunt down IS militants involved in an array of attacks across the country.
Sirte had been a stronghold of IS militants before they fled the city inland following their defeat last year by militias loyal to a UN-backed government in Tripoli, the capital.
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