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 National Human Rights Commission had issued a notice to the AP government after one of its members said it involved "serious violation" of human rights of the individuals and the firing could not be justified on the ground of self defence.
"The Tamil Nadu government has ordered a solatium of Rs three lakh to the families of each of those killed from the Chief Minister's Relief Fund," an official release in Chennai said.
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.
Also, a police team headed by IGP Manjunatha has been sent to liaison with Andhra Pradesh police to identify the bodies and conduct post-mortem, the government said.
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.
Aditya Birla plans to consolidate retail biz under one roof
I reached where no other non-Chinese could reach, says Saina
PHOTOS: Amitabh, Prince Aga Khan receive Padma Vibhushan
Smashing their way to the top
Chennai look to put behind off-field controversies, start afresh