Official sources here said that the prime minister has strongly disapproved incidents of vandalism reported from certain parts of the country.
In an advisory to all states and union territories, the Home Ministry said incidents of the toppling of statues have been reported from certain parts of the country and it has taken serious note of such incidents of vandalism.
"The MHA has asked the states that they must take all necessary measures to prevent such incidents," it said.
The ministry said the state governments were told that persons indulging in such acts must be sternly dealt with and booked under relevant provisions of law.
"Honorable Prime Minister has also spoken to the Home Minister in this regard," the advisory said.
The advisory did not specifically mention Tripura but sporadic violence and clashes have been reported between rival political groups in the state after election results were declared on Saturday.
A statue of Lenin was brought down at Belonia town in south Tripura on Monday with the help of a bulldozer after the BJP's victory in the Assembly elections in Tripura where a 25-year-long communist government was ousted.
A statue of social reformer and founder of Dravidian movement E V Ramasamy 'Periyar' was also allegedly vandalised in Tamil Nadu's Vellore district on Tuesday night.
On Tuesday, Home Minister Rajnath Singh called up Tripura Governor Tathagata Roy and DGP A K Shukla and asked them to ensure peace and check violence till a new government is installed in the state.
Union Home Secretary Rajiv Gauba had also spoken to the DGP and asked them to take all possible steps to maintain law and order, check violence and restore peace and public order.
The ministry said enough central and state forces were available at the disposal of the state government to tackle the situation.