Twenty people, several of them reportedly Tamils, were killed in the police action at Chittor district in Andhra Pradesh.
While police had claimed they had fired in self-defence, rights groups and political parties in Tamil Nadu had condemned the incident and demanded a full-fledged inquiry.
They said six of their personnel were also injured in an attack by the smugglers allegedly armed with sickles, axes and country-made weapons.
"The Tamil Nadu government has ordered a solatium of Rs three lakh to the families of each of those killed yesterday from the Chief Minister's Relief Fund," an official release here said.
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A team of revenue officials of Tiruvannamalai and Vellore led by Tiruvallur District Collector has been deputed to Tirupati to bring back the bodies. Many of those who died are from Tiruvannamalai and Vellore districts.
Hearse vans of the State government have also been sent to Andhra Pradesh to bring back the bodies.
AP government officials in Tirupati told reporters that all assistance would be provided to the kith and kin of those killed, including provision of basic amenities.
They said they were coordinating with their Tamil Nadu counterparts to ensure bodies are properly identified and taken back.