The pro-rebel Tamilnet website said one boy was killed on Thursday by government shelling in Mullaittivu.
It also said the military had conducted air raids late Wednesday over the suburbs of Kilinochchi, killing one man.
"Troops established their writ over the entire Nachchikuda village, a prominent Sea Tiger bastion," the ministry said.
The Liberation Tigers of Tamil Eelam (LTTE) had used the base in the picturesque village as a weapons hub, bringing them in on ships and then transporting them over land to the frontlines, the military said.
The Tigers withdrew from Nachchikuda earlier this week as ground troops advanced towards the village, but not before soldiers inflicted "heavy casualties", the ministry said.
There was no immediate comment from the LTTE, who have fought since 1972 for a separate state for minority Tamils in the majority-Sinhalese nation. Tens of thousands of people have died in the conflict.
Government troops are currently trying to capture the nort