Military sources said about 200 Tiger fighters were believed killed on Monday, but the military has not yet released photographs of the bodies.
Brigadier Udaya Nanayakkara said a major military operation was under way to get Velupillai Prabhakaran, whose son and several key aides were killed by special forces commandos on Monday.
"He is there and we have surrounded him -- it is a 360 degree cordon and he has no escape," Nanayakkara said.
He said Prabhakaran, 54, and his elite bodyguard were putting up stiff resistance, but the military was closing in on them.
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"The current offensive is aimed at getting Prabhakaran and the rest of the senior leadership of the Tigers," Nanayakkara said. "It is going to be a few days, or even a few hours, before we meet him.
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Military sources told AFP that Prabhakaran had been talking on his radio communication network on Monday although there had been speculation about his fate.
Nanayakkara said Prabhakaran's 24-year-old son Charles Anthony, wh