About 40 soldiers and 90 rebels were wounded in the battles outside Kilinochchi, the besieged political capital of the Liberation Tigers of Tamil Eelam (LTTE), the military statement said.
The latest clashes came a day after the Tigers said they killed 60 soldiers and wounded 150 in a counter attack on the outskirts of Kilinochchi over the weekend.
Both sides are known to make exaggerated claims about the casualties they have inflicted on each other, and independent verification is virtually impossible as journalists and aid workers are barred from the conflict area.
Sri Lanka's military also carried out air attacks against suspected Tamil Tiger targets earlier on Monday to support ground troops, the statement said.
Meanwhile President Mahinda Rajapakse asked the LTTE to allow some 300,000 civilians in rebel-held areas to move away from the fighting.
"With the dawn of 2009, the LTTE should release all innocent Tamil people it is holding hostage and in bondage using them as