More than 3,500 people have been killed in Sri Lanka in the past year.
The bitter ethnic conflict has claimed more than 60,000 lives since 1972.
Military officials said there was sporadic shelling along the district borders of Batticaloa and Trincomalee while more than 3,300 civilians fled the area and sought shelter in public buildings.
Meanwhile, the rebel Liberation Tigers of Tamil Eelam (LTTE) prepared to return the bodies of four government soldiers killed over the weekend, officials said.
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The International Committee of the Red Cross (ICRC) in a statement asked both the military and the LTTE to comply with international humanitarian law and protect civilians.
The ICRC appeal came as the LTTE said 41 civilians in areas held by them had been killed in two days of shelling by troops.
The military has denied attacking civilians and in turn accuses the rebels of using human shields.
The military said 12 soldiers were killed on Sunday.
But the Tamil Tigers had placed militar