One of the gunboats was rammed by a rebel craft packed with explosives while another was destroyed under heavy fire, spokesman Prasad Samarasing said.
The boats were escorting a larger vessel carrying some 300 troopers to the northern peninsula of Jaffna.
"We believe that the Tigers were targeting the Green Ocean vessel which was carrying 300 troops," Samarasinghe told AFP. "The navy confronted the terrorist boats. A big terrorist boat packed with explosives rammed a Dvora gunboat."
"There were some survivors, but we don't know exactly how many sailors were in the first Dvora which was sunk," Samarasinghe said. "The navy has also destroyed about eight Tiger boats."
He said helicopter gunships and supersonic aircraft were sent to the area to bomb another flotilla of boats and the military estimated that a total of 20 guerrilla boats were sunk in the ferocious sea battles.
The latest violence comes despite pledges by both sides to honour and uphold a threadbare truce in place since February 2002.
There was no immediate word from the Tigers about the sea battle.

Copyright AFP (Agence France-Presse), 2006