"Our soldiers have seen the LTTE coming with their weapons and fired at them. Not only have we recovered the bodies, we have also recovered 268 weapons."
Nanayakarra acknowledged that the army had lost "a few" soldiers in the fighting, but did not confirm the exact numbers of government casualties.
There was no immediate word from the LTTE on the military's claims and independent verification is impossible as the Sri Lankan strictly controls access to the war zone for journalists and aid workers.
However, the pro-rebel TamilNet website said that the LTTE carried out a heavy barrage of artillery and mortar fire on army positions early on Sunday and killed a "considerable number of soldiers".
The defence ministry announced on Sunday that the fighting had reached the "final phase" of operations against LTTE, which has been fighting for greater autonomy for ethnic minority Tamils in the north and east of the country since 1972.
"The fighting will end when the LTTE lays down its arms," Nanayakkara said.
"It is not possible to give a timeline because we are concerned about the civilians, but the moment we rescue the civilians it is just a matter of time."
Sri Lanka officially estimates that 70,000 civilians remain trapped in the tiny strip of land where fighting continues, but the United Nations says the number of non-combatants could be as many as 200,000.
About 500 Tamil Tiger fighters are in the area, the military says.
Another 200 civilians crossed the front lines and sought shelter with government forces on Sunday, the defence ministry said, adding that a 17-year-old girl was wounded while trying to escape.
About 36,000 people have sought shelter with security forces since January.
Also on Monday, the military said the LTTE fired artillery towards a ship flying the flag of the International Committee of the Red Cross (ICRC) that had landed food and aid supplies there.
No one was injured and the boat was not damaged, Nanayakkara said.