Troops took control of the village of Ampakamam after hours of heavy fighting, the ministry said, adding that the area had been used by the Liberation Tigers of Tamil Eelam (LTTE) as an administrative hub.
Troops moved into the area as soldiers in the neighbouring Kilinochchi district were trying to take control of the town of Kilinochchi, where the Tigers maintain their political headquarters.
The air force carried out several bombing sorties over Kilinochchi on Monday after an intense bombing drive over the weekend, the ministry said.
Last week, the military said it was within "kissing distance" of the town, but heavy rebel resistance and monsoon rains had slowed the army offensive.
Both sides have claimed inflicting heavy losses in the recent battles.
However, it is not possible to verify casualty claims by either side as independent reporters and aid workers are banned from the north.The Sri Lankan government pulled out of a Norwegian-brokered truce in January. The rebels are fighting for a separate state for ethnic minority Tamils from the majority Sinhalese community.