IS vandalised the Mosul museum after overrunning the city in 2014 and attacked sites including the ancient cities of Hatra and Nimrud, posting videos lauding the destruction online.
As Iraqi forces close in on Mosul, the jihadists' last main bastion in the country, officials say IS has fighters deployed at or near archaeological sites.
"Our information indicates that (IS) has a presence in the archaeological sites," Ahmed al-Assadi, the spokesman for the Hashed al-Shaabi, an umbrella organisation for pro-government paramilitary forces, told AFP.
The Hashed al-Shaabi, the most powerful groups in which are Iran-backed Shiite militias, launched an operation Saturday that could see it advance through IS-held areas in Nineveh province that are home to some of Iraq's most famed historical sites.
"We expect (IS) will try to lure the advancing forces to the sites for the purpose of increasing their destruction," Assadi said.
IS had earlier set up a training camp at Hatra, which is a UNESCO world heritage site, and still has militants deployed there, according to Ali Saleh Madhi, the local official responsible for the area.
- Training, arms storage -
At Nimrud, IS rigged structures with explosives and blew up the site, but the jihadists are still present nearby, said Ahmed al-Juburi, the area's administrator.
Assadi said that Hashed forces would use "extreme care" when they near the sites, and that "every effort must be made to protect and preserve them."
When the operation to retake Mosul was launched on October 17, the head of UNESCO urged parties to the conflict to protect heritage sites.
"I call on all involved in military action to protect cultural heritage and refrain from any military use or targeting of cultural sites and monuments," Irina Bokova said.
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Both UNESCO and Iraq's culture ministry said they gave coordinates of heritage sites to anti-IS forces in an effort to protect them.
Deputy Culture Minister Qais Rasheed said that anti-IS forces had been informed of sites where jihadists were present, and that IS "places weapons and sometimes trains its fighters in archaeological areas."
The lists could help limit air strikes in sensitive areas and encourage Iraqi ground forces to exercise some restraint, but they will not hold IS back.
- 'Barbaric attacks' -
Since overrunning swathes of Iraq in 2014, the jihadists have embarked on an orgy of destruction that they have justified as religiously mandated elimination of idols.
In reality, the attacks on Iraqi cultural heritage have been carried out for propaganda purposes, and IS has stolen and sold artefacts that it allegedly reviles to fund its operations.
In February last year, IS released a video showing militants armed with sledgehammers and jackhammers rampaging through the Mosul museum, destroying statues and defacing an imposing granite Assyrian winged bull at the city's Nergal Gate.
The destruction sparked international outrage.
A few months later, IS released another video shot at Hatra, a well-preserved city southwest of Mosul that is more than 2,000 years old and has a unique mix of eastern and Western architecture.
The video showed militants knocking sculptures off walls, shooting at them with an assault rifle and hacking away at a statue with a pickaxe.
A third video was released a few days later showing IS smashing artefacts at the ancient Assyrian city of Nimrud, which was founded in the 13th century, before blowing up the site.
"The demolition of the Mosul museum and the destruction of archeological remains in Nineveh will remain in human history as one of the most barbaric attacks against the heritage of humanity," UNESCO said.
"These crimes must not remain unpunished."