Mr Palaniswamy said the state government has been repeatedly taking up with Centre the various instances of arrest and "intimidation" of fishermen by the Lankan Navy, besides seizure of their boats and pressed for a lasting solution.
"I express my strong condemnation. I express my sympathies and condolences to the family of the deceased, Bridgo," he said in a statement.
Mr Palaniswamy announced a sum of Rs 5 lakh to the family of the deceased from the Chief Minister's Public Relief Fund.
He also announced Rs 1 lakh to another fisherman, who was injured in the attack, and directed that the best medical treatment be offered to him.
Mr Palaniswamy said the incident took place when the Indian fishermen were fishing in their "traditional waters" near Palk Bay and that the "Sri Lankan Navy opened fire without any warning."
The 22-year-old Bridgo was shot dead on Monday allegedly by the Lankan Navy while he was fishing in a mechanised boat at a short distance off Katchatheevu islet.
Another fisherman suffered injuries in the firing while others at the spot escaped unhurt and returned to the shore.
The Tamil Nadu government had yesterday protested the "escalation" in apprehension of its fishermen by Sri Lanka and said the Centre did "not seem to put adequate pressure" on Colombo regarding the matter.