The attack on Saturday was the worst at sea since a truce halted civil war in 2002.
Fishermen pulled two sailors alive from the water after the pre-dawn attack on the Israeli-built fast patrol boat just outside Trincomalee naval harbour, and the navy was searching for the rest of the crew, all initially feared to have died.
One of the survivors said a Tiger boat had rammed their boat and exploded, destroying both vessels, a military source said.
Harbour police said they had heard a loud explosion.
No debris found
Officials said crews searching the Trincomalee site after daylight could find no debris from the two vessels.
Commodore Jayantha Pererasaid, a navy spokesman, said: "We believe it was a Tiger suicide mission. The Dvora [a fast attack craft] was completely destroyed.
"We're still looking for the 13 missing."
"We believe it was a Tiger suicide mission. The Dvora was completely destroyed"
Brigadier Prasad Samarasinghe, a military spokesman, said it was too early to consider the missing to be dead.
If confirmed, it would be the first such attack on the military since the ceasefire. A similar attack on the navy in Trincomalee harbour killed 12 sailors and led to the collapse of a previous ceasefire in 1995.
In December, 39 military personnel were killed in a string of mine attacks, the deadliest month since a 2002 ceasefire that diplomats and truce monitors say is strained to breaking point.
The Liberation Tigers of Tamil Eelam were not immediately available for comment, but have routinely denied any hand in attacks on the military - which analysts and the government say they cannot believe.
Threat to resume struggle
The rebels have threatened to resume their armed struggle unless given wide autonomy.
Suspected rebel attacks increased after the Tigers helped destroy the chances of the candidate seen as most likely to reach a peace deal by boycotting November's presidential poll, which analysts say shows that they are using the truce to regroup and
The boycott helped Mahinda Rajapakse, a hardliner, to win the presidential election.
President Rajapakse (in front) took
office in November
Each recent attack on the military has also come on the heels of Tiger reports of army abuses and killings. The government is investigating one such incident after five Tamil youths, whom the army said were blown up by their own grenade, were found shot dead.
The Tigers say they want a political solution to the conflict, which has killed more than 64,000 people and displaced hundreds of thousands since 1983.
But they also say they are ready for war unless they are given an ethnic homeland in the north and east, where they already run a de facto state.
A peaceful settlement seems a a long way off, however. President Rajapakse's new government and the rebels are unable even to agree on a venue for talks, with the Tigers demanding that they be held in Europe and the government insisting on Asia or at home.
Erik Solheim, a Norwegian peace envoy, is due in Sri Lanka on 23 January to try to break the deadlock.