A defense ministry statement said 54 rebels and 34 soldiers were wounded in ground battles and airstrikes in the rebel strongholds of Kilinochchi and Mullaittivu.
The ministry said the casualties were among the heaviest since Army Chief Lt. Gen. Sarath Fonseka "vowed to eliminate the terrorists" from their last bastions.
There was no immediate comment on the Tamil Tiger Web sites. The ministry's claims could not be independently verified as Western journalists are not permitted in the battlefield areas.
The ministry said heavy fighting was reported in the Wanni battlefront in Kilinochchi, as troops of the 57 Division had prevented the rebels from bringing in reinforcements. The report said the battlefront stretches from the Eastern coast to the Western coast from the Nayaru lagoon toward Nachchikudda.
It claimed the rebels were "cornered and (on) the verge of extinction."
The rebels -- led by the LTTE or the Liberation Tigers of Tamil Eelam -- have been fighting since 1982 for a separate homeland for the Tamil-speaking minority on the Indian Ocean island nation. More than 65,000 people have died during that time.