Two small navy vessels were attacked about 165km north of the capital, Colombo, on Wednesday. One boat was badly damaged in the attack and four other sailors were injured.
The navy sank two Tiger boats and fought off the attack with the help of helicopter gunships, naval spokesman DKP Dassanayake said.
Officials had earlier said that no navy personnel were killed in the clash, but the Liberation Tigers of Tamil Eelam (LTTE) had prevented them from getting near the badly damaged boat where the bodies were found.
The LTTE said only one of their fighters died.
The Tigers also killed a soldier and wounded six other people, including three civilians, in two mortar attacks earlier on Wednesday in the northeastern district of Trincomalee, Prasad Samarasinghe, a defence ministry spokesman, said.
Several schools in the capital were closed as parents kept their children at home or collected them from classes after series of anonymous calls warning of bomb attacks, Keheliya Rambukwella, a government spokesman, said.
"We have made arrangements to strengthen security in the face of the terrorist threat," he said.
Police said army bomb-disposal squads were rushed to several schools, but the bomb threats were hoaxes. Police said an investigation was under way to trace the hoaxers.
Soldiers escort the hearse of the
slain Major-General Kulatunga
The bomb scares came ahead of the funeral of army Major-General Parami Kulatunga, who was assassinated by a suspected Tamil Tiger suicide bomber on Monday.
Kulatunga was the army's third in command and the most senior officer to be killed in three decades of separatist conflict.
The army has tightened security measures following Kulatunga's assassination and several checkpoints were established in the northeast to prevent the Tigers from smuggling explosives.
In other news, ceasefire negotiator Norway is expected to meet with other monitors in Oslo on Thursday to decide the future role of the Nordic ceasefire monitoring mission on the island.
Last week the Tigers demanded the removal of observers from European Union members Finland, Sweden and Denmark after the EU outlawed the group.
Norway has insisted it will continue its mediating efforts, saying withdrawal is not an option.
The Tigers fought a civil war with the government for nearly two decades until a ceasefire in 2002. They want a separate Tamil homeland in the north of Sri Lanka.