The military said three of its security personnel died in the gun battles.
In a separate incident Monday, the military said two policemen were killed in a land mine blast in Vavuniya district, the Press Trust of India reported. The military blamed the Tiger rebels for the attack, which killed the two as they drove on a motorcycle.
The weekend clashes were the latest in the campaign the military has been waging against the rebels for several weeks in the Tamil stronghold northern region.
The defense ministry was quoted as saying its security forces have killed 1,126 rebels since the start of this year, while losing 51 of its soldiers in the same period.
The Tamil Tigers have been fighting since 1983 for a separate homeland for the Tamil-speaking minority on the predominantly Buddhist island nation. The rebellion has so far claimed at least 70,000 lives.