The Sri Lankan army and Tamil Tiger rebels have blamed each other for the deaths of 10 civilians in shelling in the Muslim-majority town of Muttur.
The victims were taking shelter in a school when it was hit.
Muttur has become the centre of fierce clashes between the two sides. At least five people have been in other shelling attacks in schools and colleges.
The Red Cross says it has been told that 22,000 people have been displaced by the fighting in Muttur.
"At least 10 Muslim civilians were killed and 20 others injured as Tamil Tiger terrorists bombarded the Arabic College in Muttur town with heavy Artillery fire, " a statement from the Sri Lankan Ministry of Defence said.
But a statement form the Pro-rebel TamilNet website gave a starkly contrasting account.
Neither side accepts responsibility for civilian casualties
"At least 10 Muslim civilians who sought refuge in Arabic College in Muttur town were killed when a Sri Lankan army-fired artillery shell hit the college on Thursday around noon," it said.
Witnesses have described the north-eastern town as being shelled by both sides as each advances and then retreats.
Correspondents say that telephone communication with Muttur has been almost entirely cut-off.
Earlier the rebels said they have taken control of Muttur, but the government denied this was the case.
In an interview with the BBC, a Tamil Tiger spokesman said that the town's ferry terminal was now under their control, and attempts by the Sri Lankan navy to re-capture it had been foiled.
Full scale war
The fighting comes amid an army offensive in Trincomalee district to regain control from the Tigers of the Maavilaru waterway, which it says supplies water to 15,000 families.
Despite the upsurge in fighting both sides still say they are acting defensively and therefore within the conditions of a 2002 ceasefire.
Privately both also say they do not consider the recent violence to be the beginning of a full scale war.
But the ferocity of the fighting has meant that international agencies are unable to enter Muttur, and are now trying to negotiate a temporary ceasefire to evacuate the injured.
The Red Cross says it has been told by the government that displaced people have fled to schools and churches.
A spokeswoman told the BBC that the people of Muttur are suffering from a grave lack of medical facilities, as the main hospital in the town was not functioning.
She said that the food situation in the area "would soon become a high priority".
A resident of Muttur, Mrs Karunawathi, told Reuters on telephone that people were "very scared".
"We cannot go out. We have no food and just one bottle of water."
The BBC's Dumeetha Luthra in Colombo says there is still hope that Sri Lanka can avoid all out conflict and neither side wants to be seen as instigating the final meltdown.
The government has offered to hold talks with the rebels over the water dispute, but say they will only stop fighting if the canal is reopened. So far the Tigers have not responded to the proposal.
The rebels have shelled army positions in the latest attacks
The fighting in Trincomalee district started nine days ago when the air force began bombing Tamil Tiger positions.
At least 23 soldiers have been killed since the army launched the offensive to the south of Trincomalee port. The Tigers say they have lost 25 fighters before Wednesday's fighting.
Up to 3,000 troops are involved in the efforts to gain control of the Maavilaru waterway, reports say.