The destruction at Nimrud, located near the militant-held city of Mosul, follows other attacks on antiquity carried out by the group now holding a third of Iraq and neighbouring Syria in its self-declared caliphate.
The attacks have horrified archaeologists and UN Secretary-General Ban Ki-moon, who last month called the destruction at Nimrud "a war crime."
The seven-minute video, posted late Saturday, shows bearded militants using sledgehammers, jackhammers and saws to take down huge alabaster reliefs depicting Assyrian kings and deities.
"God has honoured us in the Islamic State to remove all of these idols and statutes worshipped instead of Allah in the past days," one militant says in the video. Another militant vows that "whenever we seize a piece of land, we will remove signs of idolatry and spread monotheism."
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The militants have been destroying ancient relics they say promote idolatry that violate their fundamentalist interpretation of Islamic law, including the ancient Iraqi city of Hatra, a UNESCO World Heritage site.
Some of the figures in the video released Saturday at Nimrud appeared to have rebar, ribbed bars of steels designed to reinforce concrete that are a technique of modern building.
An Iraqi Antiquities Ministry official, speaking today on condition of anonymity as he wasn't authorised to talk to journalists, said all the items at Nimrud were authentic. In March, both Iraqi and UN officials warned the site had been looted and damaged.
The video conformed to other Associated Press reporting about the militants' attack.
The Assyrians first rose around 2,500 BC and at one point ruled over a realm stretching from the Mediterranean coast to what is present-day Iran.
Located on the eastern side of the Tigris River, Nimrud, or Kalhu, was founded in the 13th century BC.