She also requested the Prime Minister to evolve a "permanent" and "pragmatic" solution" to end their woes.
Three fishermen in their mechanised fishing boat from Pudukottai District were apprehended by Sri Lankan Navy on Wednesday and taken to Kankesanthurai there, she said in a letter to Modi.
"I request your personal intervention and request you to direct the External Affairs Ministry to secure the immediate release of the 24 fishermen and 93 fishing boats, including three fishermen and their one mechanised fishing boat apprehended on June 15 at the earliest", she said.
She said Sri Lankan authorities "adamantly refuse" to recognise the "traditional and historic rights of our Tamil Nadu fishermen" to eke out their livelihood by fishing in Palk Bay, she said.
It was painful that Sri Lanka "is now adopting a strategy of detaining boats for long periods of time," causing immense loss to fishermen, she said.
Jayalalithaa wrote to Modi on May 31 after seven fishermen from Tamil Nadu were arrested by Sri Lankan Naval personnel and had asked him to take steps for their release. She again wrote to him on June 6 stating that the situation at sea remains "precarious" due to "offensive acts" of the Sri Lankan Navy despite repeated appeals to the Centre to ensure safety of Indian fishermen.