Iraqi workers clean an archeological site in Nimrud, 22 miles southeast of the northern city of Mosul, in July 2001.  (Karim Sahib/AFP)

The Islamic State's destruction of cultural antiquities in Iraq has stepped up a notch recently, with members of the extremist group both bulldozing the 3,000-year-old Nimrud archaeological site near Mosul and ransacking the similarly ancient ruins of Hatra in the past few days.

Now, the United States' top military officer has said the U.S.-led coalition against the Islamic State would "consider" intervening to protect such sites. But Gen. Martin Dempsey stopped far short of any promises – and added that any action would have to "fit into the priority of all the other things we're being asked to do on behalf of Iraq."

Dempsey – who was on a day-long visit to Baghdad, Iraq, during which he was joined by reporters including The Post's Missy Ryan – made his remarks after Iraq's antiquities ministry acknowledged reports of a third attack, on the ancient city of Dur Sharrukin, and called on the international community to intervene to stop the Islamic State from  “erasing the history of humanity.”

“We have warned previously and warn now that these gangs with their sick, takfiri ideology will continue to destroy and steal artifacts as long as there is no strong deterrent, and we still await a strong international stand to stop the crimes of Daesh that are targeting the memory of humanity," the ministry said in a statement published by the Guardian, using the Arabic acronym for the group.

Separately, Iraqi Tourism and Antiquities Minister Adel Shirshab told reporters that only the U.S.-led coalition had the power to protect these sites. "Our airspace is not in our hands. It's in their hands," Shirshab said on Sunday, according to Reuters, alleging that coalition aircraft could have monitored attacks on archaeological sites and prevented them.

The U.S. government is well aware of the threat to antiquities posed by ongoing violence in Iraq and Syria – last year, the U.S. Department of State and the American Schools of Oriental Research (ASOR) signed a deal to document that damage caused to Syria's cultural heritage sites. There have also been a number of internal attempts in Iraq and Syria to defend sites that might be at risk, including the covert work of a group of preservationists dubbed modern-day "Monuments Men."

However, Dempsey, chairman of the Joint Chiefs of Staff, didn't hint at any impending military action to save sites under threat by the Islamic State. Instead, he told reporters that any requests made by the Iraqi government to protect such sites would have to be weighed against other priorities – including preventing attacks on civilians or protecting key infrastructure.

The Islamic State currently holds vast swaths of Iraq and Syria within its control and with it many important archaeological finds from ancient Mesopotamia. The group's puritanical view of Islam holds that such pre-Islamic antiquities are heretical or forms of idolatry and that they should thus be destroyed.

Last month, in a video that showed the destruction of ancient artifacts in the Iraqi city of Mosul, one of the Islamic State fighters bragged about the damage they had caused."We do not care even if it costs billions of dollars," the fighter explained: His point was undercut, however, by reports that almost 100 Syrian artifacts looted by the Islamic State have been smuggled into Britain and sold to raise money for the group.