Both clashes occurred in the area around Vavuniya, the Press Trust of India reported.
Four soldiers died in a mine explosion in the area and two more were wounded. Three soldiers were killed in an ambush along the Vavuniya-Medawachchiya Road.
The government also reported that 11 militants were killed on Tuesday in another fight.
Vavuniya, the major town in a heavily Tamil area, is a frequent site of fights between the Liberation Tigers of Tamil Eelam or Tamil Tigers and the army.