According to antiquities specialists, Daesh relies on trafficking as source of financing and only destroys the pieces that are impossible to sell or transport.
The ruins of the city founded in the 13th century BC were one of the most famous archaeological sites in a country often described as the cradle of civilisation.
Nimrud, which is on UNESCO's tentative list of world heritage sites, is the later Arab name given to a settlement which was originally called Kalhu.
The ancient city was first described in 1820 and plundered by Western explorers and officials over subsequent decades. It was also looted and damaged during the 2003 US-led invasion of Iraq.
The bulldozing that took place at the Nimrud site in early March came days after another video was released showing Daesh militants destroying artefacts at the Mosul museum.
That attack sparked widespread consternation and alarm, with some archaeologists and heritage experts comparing it with the 2001 demolition of the Bamiyan Buddhas in Afghanistan by the Taliban.
- War crime -
The first militant seen talking in the video criticises the international community over its reaction to Daesh' destruction of statues and artefacts.
He mentions media coverage showing "worthless people crying because we broke idols" and "portraying believers as if they were barbarians who do not care about culture and civilisation."
UNESCO and other organisations have called for an urgent global mobilisation to save what could still be saved from the jihadists but experts agree little can be done short of a ground operation to retake land under Daesh control.
The UN cultural agency's chief, Irina Bokova, had said in early March that the bulldozing at Nimrud amounted to a war crime.
She travelled to Baghdad on March 28 to step up measures aimed at protecting heritage, such as carrying out inventories and using satellite imaging and remote sensing.
In Saturday's video, an Daesh militant vows the group will press on with its campaign against heritage sites.
"I swear to God, we will remove the signs of idolatry until we destroy the shrines and the graves of the Rafidha (a derogatory term for Shiites) in their own heartland, break the crosses and destroy the black house in the heartland of infidels, America," he said, referring to the White House.
Daesh released another video on April 3 in which militants are seen damaging artefacts at Hatra, a well-preserved city with a unique mix of eastern and western architecture, located in a desert area southwest of Mosul.