The government rejected the last-ditch call for a cease-fire, saying the thousands of civilians trapped in the war zone all have escaped to safety and there was no longer any reason to stop the battle.
With the war nearing its end, Sri Lankans poured into the streets in spontaneous celebration.
President Mahinda Rajapaksa scheduled a nationally televised news conference for Tuesday morning at Parliament, where he was expected to tell the nation the war was over.
The fate of the Tamil Tigers' top commanders remained unclear, including the whereabouts of the reclusive rebel leader Velupillai Prabhakaran.
A senior military official said troops found the bodies of several rebel fighters who had committed suicide Sunday when troops surrounded them.
The bodies were suspected of being Prabhakaran and his deputies, but the military was still trying to confirm their identities, the official said, speaking on condition of anonymity because he was not authorized to speak to the media.
The rebels, who once controlled a wide swath of the north, have been routed by government forces in recent months.
On Sunday, Tamil Tiger suicide bombers targeted troops clearing out the last pockets of rebel resistance in the war zone and troops killed at least 70 rebels trying to flee, the military said.
On Sunday afternoon, the tattered and nearly defeated rebel group offered to lay down its arms, saying it was acting to protect the wounded in the war zone. -- AP