He said six fishermen from Rameswaram had ventured out for fishing in a mechanised boat on November 13.
"It is reported that while fishing within our territorial waters, about four nautical miles from the shore near Olakkuda around 3.15 pm, an Indian Coast Guard (ICG) ship 'Rani Abaka' asked the fishermen to stop their boat for inspection and fired at the fishing vessel," he said in his letter to Modi, a copy of which was released to the media here yesterday.
The chief minister said they were admitted in the General Hospital at Rameswaram and were undergoing treatment.
"A bullet was found in the fishing vessel and was handed over later to the Mandapam Marine police station," he said.
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The fishermen had also alleged that the Coast Guard personnel got into their vessel, manhandled them and hit them with sticks and iron rods, he said.
"The Mandapam Marine police station has registered a First Information Report on the incident on November 14, based on the complaint filed by the injured fishermen," Palaniswami said.
Reiterating the issue of apprehension of fishermen and confiscation of their boats by Sri Lanka, the chief minister said against this background, the Coast Guard personnel could have shown better restraint.
"Hence, I request you to immediately intervene in this matter and advice the Ministry of Defence to avoid such incidents in future," he said.
Tamil Nadu IT Minister M Manikandan had told PTI on Tuesday that the matter would be taken up with the Centre to ensure that such incidents did not recur.
The Coast Guard while denying any firing by its personnel had said that the fishing crew in question was involved in "unauthorised" paired trawling.
A Coast Guard vessel on patrol off International Maritime Boundary Line in Palk Bay "was routinely" investigating fishing boat 'Jehovah Jireh', its statement had said.
The vessel was investigating the boat "for paired trawling on November 13, 2017, at about 1440 hrs," it said.
A Madurai report said two Coast Guard Junior Commissioned Officers called on the fishermen at the hospital, enquired about their health and the firing incident, following which the fishermen reportedly decided to call off the stir.
Fishermen Association's president N J Bose was also present.
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