Keheliya Rambukwella, the policy planning minister, said security forces had moved into Sampur, 10km across the Koddiya Bay from the Trincomalee naval and air complex on Monday, with hardly any resistance.
"We captured the main Sampur artillery position of the Tigers," said Rambukwella who is also the government's defence spokesman.
"We suspect they dismantled the guns or pulled them back. We are now in Sampur."
He said troops had moved in on Monday after a lull in fighting on Sunday.
However, a soldier was killed and several others were wounded in an overnight mortar bomb attack against security forces in the area, military officials said.
The military had virtually suspended a ground advance towards Sampur at the weekend, following weeks of fighting after intense rebel resistance.
But the air force pounded the area using Israeli-built Kfir fighter jets, clearing the way for ground troops to walk in, officials said.
"Troops are now engaged in clearing operations"
Keheliya Rambukwella, policy planning minister
"Troops are now engaged in clearing operations," Rambukwella said. "The only resistance we encountered was mines and booby-trapped devices."
"Our objective is not to take land, but to neutralise these three guns in the national interest," Rambukwella said.
There was no immediate word from the Tigers on the military claim.
Fighting in Sri Lanka has intensified since December, shattering a ceasefire in place since 2002 and leaving more than 1,500 dead, according to official figures.
Both sides have pledged to uphold the truce and accuse each other of mounting offensive operations.
More than 60,000 people have died in the past three decades in the ethnic war for a Tamil homeland.