"A helicopter of the border guard service crashed. There are dead," the Chechen government said in a statement, adding that officials were verifying the number of casualties.
The accident occurred at high altitude during a routine flight as the Mi-8 helicopter was preparing to land, investigators said in a separate statement.
In a message on social media, Chechen strongman Ramzan Kadyrov sent his "deep condolences" to the families of the victims.
When reached by AFP, a spokesman for military investigators, Sergei Zhukov, said investigators had yet to reach the scene of the crash.
While the violence has largely died down, Chechnya and other parts of the Russian Caucasus remain the site of a simmering insurgency by Islamist militants against the pro-Kremlin local authorities.
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