The External Affairs Ministry here also said that 184 pilgrims will be returning to Sri Lanka from Tamil Nadu on a special flight.
Issuing a travel advisory, the ministry said, "the government of Sri Lanka regrets the increasing number of instances of intimidation of Sri Lankan nationals visiting Tamil Nadu for the purposes of tourism, religious pilgrimages, sporting and cultural activities and professional training.
"These visits are a reflection of people-to-people contact between the polity of two countries which are bound by age-old friendly ties and traditions."
The government here is constrained to request Sri Lankan nationals in the interest of their security to desist from undertaking visits to Tamil Nadu until further notice, it said.
In the event there is a compelling reason to visit Tamil Nadu, such a visit should take place following prior timely intimation to the Sri Lanka Deputy High Commission in Chennai, the ministry said.
A Rajakaruna, an official of the Sri Lankan Deputy High Commission in Chennai, told local media here on the phone that all other Sri Lanka-connected institutions in the Tamil Nadu capital were safe.
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He said special security has been provided at the Mahabodhi Society offices in Chennai, a prominent Buddhist religious institution.
Tamil Nadu Chief Minister Jayalalithaa has been urging the Centre to curtail training for visiting Sri Lankan defence officials in the state. She also ordered the return of a Sri Lankan football team.