The government said on Thursday that it is ready to negotiate with the rebels to resolve a bitter water dispute in which the Tigers had imposed a canal blockade depriving some 15,000 families of water in the Trincomalee district.
Local officials said troops had not managed to reopen the sluice gates as the area is heavily mined.
The Red Cross told Aljazeera.net on Thursday that up to 20,000 people were on the move because of the fighting.
Troop reinforcements had been moved to Muttur where thousands of families have reportedly left their homes and sought shelter in public buildings, officials said.
Tamilnet.com claimed the fighters, who want to carve out a separate homeland for Sri Lanka's 3.2 million minority Tamils, had taken control of parts of Muttur, a government-held town bordered by Tamil-controlled villages and jungle.
"The window is open," Keheliya Rambukwella, a spokesman for the government told reporters. "If the Tigers are ready, we are ready too to start talks immediately...we do not want to go back to war."
Erik Solheim (L) repeated calls to
both sides to end the hostilities
Anura Yapa, the government's media minister, also pledged commitment to the Norwegian-backed peace process.
"We will make all endavours to make sure that the peace process is not derailed," Yapa told reporters.
The conciliatory move came as peace broker Norway tried to salvage what was left of a 2002 truce. Both sides have said they are still committed to it.
Norway's top peace broker, Erik Solheim, has repeated a call to both sides to end the hostilities and resolve the water dispute through negotiations.
The Norwegian embassy said Oslo's special peace envoy Jon Hanssen-Bauer was due in Colombo Friday to hold talks with both sides.
The call for talks came just hours after artillery fire hit three schools in a northeastern Sri Lanka town where residents had taken shelter to escape fighting, killing 18 people, military officials said.
Ten people were killed at one school and 50 wounded where civilians were sheltering after security forces asked them to move to public buildings as troops battled Tamil Tiger
"The shells were falling in the town from both sides. I saw five or six people dead. It's very bad. You can't go out in the streets. We fled to the beach"
Mohamed Ali Pittchikutti,
a Muttur resident
resistance, officials said.
Two constables and two paramilitary troopers attached to the local police were also killed in the clashes in Muttur, officials said.
The defence ministry said the shell that killed the civilians came from the Tigers while the pro-rebel Tamilnet.com website said the attack had been initiated by the military.
"The shells were falling in the town from both sides," said Mohamed Ali Pittchikutti, 53, shaking as his 11-year-old son Nasim was taken into surgery after being wounded when a shell hit their house.
"I saw five or six people dead. It's very bad. You can't go out in the streets. We fled to the beach."