Sri Lankan Naval personnel arrested 23 fishermen from Kottaipattinam in Pudukottai district at Neduntheevu close to the Lankan coast and the remaining 11 near Katchatheevu, an islet in the Palk Strait, fisheries officials said in Rameswaram.
The fishermen and their seven boats were handed over to the fisheries inspection offices in Jaffna and Mannar, according to the Sri Lankan Navy.
Expressing shock over the arrests, Jayalalithaa shot off a letter to the PM, terming the action by Sri Lankan Navy as "unjustified" and sought his intervention to secure their release.
"I have repeatedly and emphatically pointed out that the unconstitutionality of the Indo-Sri Lankan agreements of 1974 and 1976 and the ceding of the Katchatheevu islet, is the root cause of the problem," she said.
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"The arrest and detention of these fishermen who were peacefully engaged in fishing activities in their traditional fishing waters is unjustified," she added.
Jayalalithaa urged Modi to direct officials concerned in the External Affairs Ministry to contact their Sri Lankan counterparts and ensure that the fishermen were released along with their 46 boats.
She also reminded the Prime Minister of her earlier demand of a Rs 1,520 crore special package for deep sea fishing.
"I request you to immediately act on our long pending demands for a sustainable solution to this vexatious issue," Jayalalithaa said.