"The action of Sri Lankan Navy in detaining our fishermen will only escalate the tensions between the two countries, besides causing immense anxiety and unrest among the fishing community," she said in a letter to Singh.
She said 22 fishermen from Nagapattinam and 18 from Karaikal in Puducherry, who were engaged in fishing in the Bay of Bengal in five mechanised boats, were reported to have been apprehended by the Lankan Navy on December 3.
The Indian Navy has also confirmed their arrest, she said.
"I am deeply pained to point out that the incidents of apprehension and harassment of innocent Indian fishermen have become a regular occurrence in the past few months, creating a feeling of insecurity and fear among the fishermen community," she said.
Noting that Sri Lankan fishermen, who poach in the Indian EEZ (Exclusive Economic Zone) were warned and sent back whenever such incidents occur in the vicinity of Tamil Nadu, Jayalalithaa said, "No apprehension of Sri Lankan fishermen has occurred in the Tamil Nadu waters in the recent past".
"The Sri Lankan authorities should also reciprocate the gesture of goodwill and release the Tamil Nadu fishermen immediately, after ascertaining the genuineness of these apprehended 40 fishermen," she said.
Jayalalithaa requested the Prime Minister to urge Colombo to immediately release the 40 fishermen and their five boats without filing any cases against them.
Sri Lankan Naval spokesman Kosala Warnakulasuriya had said on December 3 that about 37 Indian fishermen were arrested and five boats were seized off the eastern coast of Pulmoddai.