It was not possible to independently verify the military's claims as the fighting took place deep in the northern jungles, where access is restricted.
Both sides often release inflated casualty figures for their opponents while lowering their own.
Violence has intensified in the Indian Ocean island nation since the government announced early this month that it was scrapping a six-year-old ceasefire between the government and the Tamil Tigers, a pact that had largely been ignored in recent years. The truce officially ended last Wednesday.
At least 36 insurgents and one soldier were killed in weekend clashes across the island's northern region, a flashpoint in the country's ethnic, separatist war.
Senior military officials have vowed to dismantle the Tigers' de facto state in parts of the north this year, and to then hunt down those that remaining fighting in the jungle.
More than 400 people have been killed in renewed violence across the country since the government withdrew from the truce, according to military figures.
The Tigers have been fighting since 1983 for an independent state in the north and east for the country's ethnic Tamil minority after decades of being marginalsed by Sinhalese-dominated governments.
The fighting has killed more than 70,000 people.