Monday's fighting in the regions of Mannar and Vavuniya also wounded 10 Tiger rebels and 18 government troopers, the ministry said.
However, the Liberation Tigers of Tamil Eelam (LTTE) said they killed 26 soldiers during Monday's clashes in the two areas.
The rebels said 20 soldiers were also killed in ground battles in Mannar on Sunday.
"The Sri Lankan army withdrew their fighting units after a few hours of stiff resistance by the Tigers," the LTTE was quoted as saying on the pro-rebel Tamilnet.
com website. The report did not give rebel casualties.
The latest fighting raises the number of rebels killed by security forces since the start of the year to 4,176, according to defence ministry figures.
A total of 353 soldiers were killed during the same period, it says.
The casualty figures cannot be verified as the Sri Lankan government restricts the movements of journalists.
The Tamil Tigers began their armed struggle for a separate Tamil state in 1972. Tens of thousands of people h