Referring to the latest incident, she said fishermen in 45 boats fishing near Katchatheevu on June 26 were harassed by Sri Lankan Navy personnel.
They reportedly chased the fishermen away after cutting the ropes and damaging nets of 10 boats, resulting in a huge loss to the fishermen, she said in a letter to Singh.
"You are aware that I have brought to your kind attention the various incidents of attack on Indian fishermen from Tamil Nadu by the Sri Lankan Navy/miscreants within the past 12 months and sought your intervention," she said.
This latest incident of harassment has shocked the state of Tamil Nadu and created a "psychological fear" in the minds of the fishermen, she said.
"I wish to reiterate that from time immemorial fishermen of Tamil Nadu have been traditionally fishing in the waters near Katchatheevu, notwithstanding any geographical or political boundaries," she said.
The Chief Minister requested Singh to take up the issue with Sri Lanka and impress upon them the need to instruct their Navy to exercise restraint and refrain from harassing "innocent" Indian fishermen pursuing their livelihood in their traditional waters, she said.
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Katchatheevu, an islet on the Palk Straits, was ceded to Sri Lanka by India in 1974.
Sri Lanka has been objecting to Tamil Nadu fishermen fishing in that area.