The Tiger guerrillas are battling to hold back a military assault that has pushed them into a 21 square kilometre (eight square mile) patch of land in the northeast of the island.
"With the fall of Pachchapulmudai (village), the LTTE lost their last supply route used for reinforcement and logistic transportation to Puthukkudiriruppu junction," the ministry said.
It said troops recovered the bodies of 13 rebels killed on Wednesday. Battlefield casualty claims are impossible to verify as journalists are not allowed to travel freely in the area.
The United Nations and foreign aid organisations say as many as 150,000 civilians may be unable to escape in the combat zone, although the Sri Lankan government insists the figure is less than half that.
At the height of their power in the mid-1990s, the Tigers controlled more than a third of the total land mass of Sri Lanka as they pushed for an independent Tamil homeland.