Fighter jets pounded suspected Liberation Tigers of Tamil Eelam (LTTE) locations in the north of the island, where heavy artillery duels killed at least one soldier and wounded another 12, the ministry said.
Both sides traded heavy weapons fire across a defence line in Vavuniya district, the ministry said.
"It is confirmed that many LTTE terrorists were killed," the ministry said in a statement.
There was no immediate comment from the Tigers.
The clash Saturday at Thampanai came three days after security forces wrested control over the final rebel base in the east of the island.
The LTTE admitted on Thursday losing Thoppigala in the district of Batticaloa, but said it would now would revert to guerrilla tactics in the troubled region.
Fighting across Sri Lanka has worsened since the breakdown of a 2002 truce around 19 months ago.
Sri Lanka's 35-year-old conflict has claimed more than 60,000 lives, and over 5,200 people have been killed in fighting in the past 19 months, acc