After demanding an emergency meeting of the Security Council, the head of the United Nations' cultural body said the International Criminal Court should also take action.
UNESCO chief Irina Bokova described the destruction as "cultural cleansing".
Iraqi Prime Minister Haider al-Abadi called it a "provocation" to the entire world which he warned would "not to unpunished".
French President Francois Hollande joined the chorus of condemnation, saying: "What the terrorists want to do is destroy all of humanity."
The Islamic State group has controlled Iraq's second city since June and has destroyed several historical and cultural sites across the country, including Muslim shrines.
In the jihadists' extreme interpretation of Islam, statues, idols and shrines are a material corruption of the purity of the early Muslim faith and amount to recognising other objects of worship than God.
Their views are marginal, however, and most clerics, even those who promote a rigorist Islam, argue that what were idols in the days of the Prophet Mohammed are now part of cultural heritage.
- Religious justification -
A bearded militant talking to the camera in the video released on Thursday argues that the destruction happening behind him is a repeat of when the Prophet Mohammed destroyed statues of idols in Mecca almost 1,400 years ago.
"The artefacts and statues in the Mosul museum are not idols of gods, but statues of kings, animals, and birds," said Radwan al-Sayyed, professor of Islamic sciences at the Lebanese University.
"Even if they were statues of gods, they are in a museum, and the Koran calls on drawing lessons from them because they were for people who have long passed and that teaches you that life is finite."
The Egyptian body which rules on Islamic law condemned the destruction of the Iraqi artefacts.
"Such antiquities are to be found in all of the countries conquered by Muslims, but the prophet's companions did not order their destruction or even authorise anything approaching it," said Dar al-Ifta, whose rulings are sought by Muslims from around the world.
Some of the statues destroyed in the video were likely replicas of pieces that had been moved to safety or are kept in museums in the West, experts say.
But several were originals, including the colossal granite Assyrian winged bull at Nergal gate in central Mosul which jihadists armed with a jackhammer can be seen defacing.
After wrecking the giant statue, IS militants reportedly told the guards of the vast archaeological site that the ancient city of Nimrud, south of Mosul, was next on their list.
- More destruction -
"It is one of the very important Assyrian capitals. There are reliefs and winged bulls there... This would be a real disaster," said Abdelamir Hamdani, an Iraqi archaeologist at New York's Stony Brook University.
He voiced fears the jihadists would also target Hatra, a UNESCO-listed site in IS-controlled territory around 100 kilometres (60 miles) southwest of Mosul.
UNESCO says the remains of Hatra, "especially the temples where Hellenistic and Roman architecture blend with Eastern decorative features, attest to the greatness of its civilisation."
On Thursday, IS militants blew up a 12th century mosque, purportedly because it contained a tomb.
They have also destroyed much of the Mosul library's collection, some of the city's best-known shrines, and historical sites elsewhere in the country.
"This is not the end of the story and the international community must intervene," Hamdani said.
US and other Western air forces operate in the Mosul area to provide support for Iraqi Kurdish and federal forces working their way towards the city.
Mounir Bouchenaki, the director of the Bahrain-based Arab Regional Centre for World Heritage, admitted it would be hard to physically protect Hatra, Nimrud or other sites in IS areas.
"If you don't have people on the ground, it's very difficult and you even risk contributing to the destruction," he said.
Arab League chief Nabil al-Arabi called the vandalism "one of the most odious crimes committed in our day and age against the heritage of humanity".
Paris's Louvre museum said IS had hit at the heart of "humanity's memory".