"Miscreants have already torched, vandalised and carried out destructive activities" on state broadcaster BTV, the national disaster management agency, police structures and other government buildings, the statement said.
The statement was issued late Thursday after the imposition of a nationwide internet shutdown that cut off Bangladesh's lines of communication with the outside world.
"So far, we have shown maximum restraint," police said, adding that if the destructive activities continued, they would "be forced to make maximum use of law".
Thirty-nine people have died this week in the clashes, sparked by student protests over civil service hiring rules, with 32 killed Thursday in the deadliest day of unrest so far.
Private broadcaster Independent Television said 702 people had been injured during Thursday's clashes including 104 police officers and 30 journalists.
At least 26 of the country's 64 districts saw clashes on Thursday, the network said.