"We have found no dead bodies. They must have burnt. Everything has gone down."
He said the 70-75 metre-long ship caught fire after the navy returned rebel fire about 190 nautical miles (350km) south of the southern port of Galle.
The Tigers were not immediately available for comment.
The incident came after the navy said it sank two small Tiger vessels in a clash off the northeast coast overnight that killed about 15 Tiger fighters.
It also comes a day after the Tigers slightly injured the Italian and US ambassadors and the UN representative to Sri Lanka when they shelled a delegation of diplomats led by the island's human rights minister to the restive east.
Assassination attempt
The Tigers say they did not know the ambassadors were on board helicopters they fired at in the eastern district of Batticaloa, and said they were provoked by army fire.
The military accused the Tigers of trying to assassinate the diplomats.
The Media Centre for National Security said in a statement overnight: "The Tigers, being severely beaten by the security forces in the east, had shown their desperation once again by trying to assassinate high-level foreign diplomats by shelling at them with mortars."
It is believed to be the first time Western envoys have been caught up in the conflict since the rebels began fighting for a separate state in 1983.
But there have been a spate of similar situations in recent months, when the Tigers shelled journalists taken to the northern frontline and the military shelled the head of the island's Nordic truce monitors when he visited Tiger territory.
Ban Ki-moon, the UN secretary-general, condemned Tuesday's attack.
But the Tigers have repeatedly ignored calls to halt a conflict that has killed about 68,000 people over the past two decades - 4,000 in the past 15 months alone.
The Sri Lankan government, backed by Mahinda Rajapakse, the president, says it will unveil a power-sharing proposal within weeks, but has rejected the Tigers' demands for a separate homeland and analysts fear the war could continue for years.