Military spokesman Brigadier Prasad Samarasinghe said 66 separatists and 13 soldiers had been killed and at least 79 soldiers wounded since Sunday, when the army, navy and air force launched a combined operation to retake Tiger-held Sampur.
The separatists said air strikes and shelling on Monday killed 20 civilians in the Sampur area, in northeast Trincomalee district, but did not say how many guerrillas were killed.
Samarasinghe denied there were any civilian casualties.
It is virtually impossible to independently confirm casualty reports because conflict zones are restricted and European monitors of a 2002 truce have withdrawn from their Trincomalee office, citing deteriorating security.
The push to retake Sampur opens a new front in the more than two-decade conflict between ethnic Tamil Tiger separatists and the Sinhalese-dominated government, which was temporarily halted by a 2002 ceasefire.
Samarasinghe said the military and Tigers traded artillery fire overnight, and that the operation was ongoing to loosen the separatists' hold on the area south of Trincomalee naval base and specifically to destroy their fire power.
"Our aim is to neutralise artillery and heavy mortar bases. Yesterday we destroyed a minimum of three artillery bases," Samarasinghe said on Tuesday, accusing the separatists of "firing at the naval base and also at civilians in the area".
The country's top-ranking military official, Lieutenant-General Sarath Fonseka, said on Monday that the operation was intended to safeguard the strategic Trincomalee harbour and navy base.
He said the separatists had been using four villages south of Trincomalee to fire artillery and mortars at the base.
"If they continue to attack the harbour it will paralyse the Trincomalee to Jaffna supply route," he said.
The Sri Lankan military relies on the Trincomalee port to supply its more than 43,000 troops on the Jaffna peninsula, as the road link passes through Tiger-held territory.
The Tigers took up arms in 1983, saying the country's 3.2 million Tamils needed a separate homeland away from the discrimination of the majority Sinhalese.
The resulting conflict cost the lives of at least 65,000 people before the 2002 ceasefire halted large-scale fighting.
In recent months, however, Sri Lanka has returned to the brink of full-scale war, with both sides launching major military offensives, although neither has officially withdrawn from the ceasefire.
Hundreds of combatants and civilians have been killed since late July, and 204,000 people have been displaced by near-daily air strikes and shelling.