The bitter ethnic conflict has claimed at least 60,000 lives since it began in 1972.
Troops were advancing into an area held by the Liberation Tigers of Tamil Eelam (LTTE) in the district of Batticaloa, Tiger spokesman Rasiah Ilanthiriyan said by telephone from the rebel-held north.
"The military has launched a ground offensive to capture real estate," Ilanthiriyan said. "They have come up to our defence line at Vakarai.
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He had no immediate details of casualties, but said the military was also shelling the rebel-held areas.
There was no immediate comment from the military.
Security forces had been accusing the guerrillas of firing artillery and mortar bombs towards army camps in the district in recent weeks.
The LTTE and the Sri Lankan government have escalated fighting in the past year in tit-for-tat battles that have claimed thousands of lives despite a 2002 ceasefire agreement.