A patrolling "fast attack" naval craft came under fire from the vessel 50 nautical miles (92 kilometres) north of Udappuwa, he said.
"We returned fire and the trawler exploded in a huge ball of fire, and sank.
Our sailors suspect there were four to five people aboard the trawler."
There was no confirmation of the report from the rebel Liberation Tigers of Tamil Eelam (LTTE).
The clash, in the narrow strait separating India and Sri Lanka, came a day after President Mahinda Rajapakse sounded out New Delhi about stepping up maritime patrols to prevent cross-border terrorism.
Rajapakse, who began a five-day working visit to India Sunday, told reporters he planned to talk to Indian leaders about strengthening patrols along the Palk Strait.
"I will be explaining my position to them -- we want joint patrolling with India in the sea because not only arms are being smuggled into our country, but drugs are also coming," the president said.
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"If the Tigers get stronger, that will be a threat