The chief minister's directions comes amid a spate of incidents targeting statues and busts of icons in the country.
"Maintaining law and order is the priority of the state and the government will take strict action against those involved in vitiating it. District police chiefs should remain alert and ensure security of statues of icons," he said in Lucknow.
Strict action should be taken against those involved in the Meerut incident and measures should be taken to ensure that such incidents do not recur, Mr Adityanath said.
In Kolkata, a bust of Jana Sangh founder Syama Prasad Mookerjee was damaged yesterday following the razing of statues of Soviet icon Vladimir Illyich Lenin in Tripura.
The bust of Dravidian movement founder EV Ramasamy Periyar in Tamil Nadu's Vellore was also desecrated, triggering widespread protests across the state.