The Sri Lankan navy, however, denied the allegation, saying it does not open fire at poaching fishermen and only arrests them.
The navy's reaction comes after India said that a 22-year-old fisherman from Tamil Nadu had been killed and another injured after Sri Lanka Navy personnel fired at them.
The Sri Lankan Fisheries Minister Mahinda Amaraweera wrote to the Secretary to the Ministry of Defence to carry out an investigation on the alleged shooting.
Amaraweera said he had spoken with Indian High Commissioner in Colombo Taranjith Singh Sandhu and assured that Sri Lanka was keen not to allow the good relations between the two countries hampered by any incident.
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There was no response from the Prime Minister Wickremesinghe's office on the Indian media reports that New Delhi had taken up the matter with him.
Indian fisherman Bridgo along with others was fishing near the Katchatheevu islet when the Sri Lankan naval personnel arrived at the spot and opened fire, fisheries department officials in Tamil Nadu had said.