In wake of the incidents, Chief Minister Yogi Adityanath instructed all District Magistrates and district police chiefs to ensure that there was no repeat of such incidents.
Of the two incidents in the past 24 hours, one took place at Trivenipuram locality of Jhusi in Allahabad where a statue's head was chopped off while the other was reported at Siddharthnagar's Gohaniya where the hand of a statue was found broken.
Locals staged a demonstration against the vandalism in Siddharthanagar, demanding immediate arrest of the miscreants.
Police officials told IANS that a case has been registered in both incidents.
In a missive to all district officials, routed through the Home Department, the Chief Minister said all efforts should be made to ensure that communal peace and harmony was not disrupted.
He also asked officials to involve public representatives and influential people of the areas in their efforts to ensure such incidents do not take place.