A letter was circulated to all states on February 28.
The Ministry also asked all states and UTs to keep vigil on social media activities of extremists.
Shia mourners took to the streets in various parts of India on Sunday to express outrage and grief.
The Union Home Ministry has asked states to keep an eye on pro-Iran radical preachers giving inflammatory statements that may result in violence in the wake of the Israel-US attack on Iran, officials said.
In a letter circulated to all states on February 28, the Ministry also asked all states and UTs to keep vigil on social media activities of extremists and global terror group handles, they said.
Advising the states to ensure that no law-and-order issues arise, the ministry has asked the states to heighten vigilance, as global events might have a domestic ripple effect through rhetorical statements, they said.
The circular asked the states to increase security at consulates, embassies, and other diplomatic offices of the USA and Israel in their jurisdictions, and at other entities of the two countries to prevent any untoward incident and maintain peace and tranquillity.
Shia mourners took to the streets in various parts of India on Sunday to express outrage and grief over the death of Iranian supreme leader Ayatollah Ali Khamenei in a US-Israel strike.
