Fighter planes gave air support to ground troops advancing toward rebel-held areas in Mannar district and bombed a suspected guerrilla training facility in the area, the ministry said.
Troops killed at least nine rebels during sporadic clashes in the tense northeastern Wanni region on Tuesday, according to the ministry which placed its government losses at five soldiers wounded.
There was no immediate comment from the Liberation Tigers of Tamil Eelam.
Tuesday's fighting raises the number of rebels killed this year by Sri Lankan forces to 3,640, according to the ministry, while 272 security forces personnel have died in combat over the same period.
Fighting has worsened since the government in January pulled out of a tattered six-year truce with the rebels.
Prime Minister Ratnasiri Wickremanayake late Tuesday vowed to press ahead with the military campaign in the north and ruled out a peace accord.
"We are not going to have any type of ceasefire agreement in Sri Lanka i