Brigadier Prasad Samarasinghe, a Sri Lankan military spokesman, said: "We have destroyed three satellite camps and are clearing the area. There are a lot of minefields."
"One Tamil civilian in the area said there are 73 prisoners being held by the Tigers there, including one army corporal."
Samarasinghe estimated that around 150 Tiger fighters remained in the Thoppigala area.
The clash on Tuesday came hours after the navy said it had destroyed five Tiger vessels after being attacked by two dozen rebel boats off Sri Lanka's northern army-held Jaffna peninsula.
Tuesday's sea battle off Point Pedro, which is cut off from the rest of the island by Tiger-held areas, was the latest in a string of land and sea battles and air strikes in recent months.
A navy spokesman said more than 40 Tigers were "presumed dead". "We destroyed five boats and damaged seven to eight more."
"They were trying to attack our patrol boats, but they failed," DKP Dassanayake said, adding that no navy vessels were damaged.
The spokesman said 24 Tiger boats, including four suicide boats, were involved in the attack and the Sri Lankan navy was trying to recover one boat which was drifting.
A Tigers source, reported by the Reuters news agency, rejected the navy's figures.
"According to our people, they managed to damage one of the Sri Lankan navy [attack boats]," the source said.
"The Sea Tigers lost two of their men and there is no damage to any of their boats reported."
Also on Wednesday, Sri Lanka's government blocked access to a popular pro-rebel website, a move decried by a media rights group as "a significant turn in the erosion of media freedom".
Acting on government orders, all of Sri Lanka's major internet service providers have blocked the TamilNet website, according to the independent Free Media Movement.
The site is popular among diplomats and journalists seeking the Tamil Tiger rebels' perspective on the decades-long separatist conflict with the government, although both sides are accused of misreporting the facts.
Fighting in Sri Lanka is now focused on the north after the military captured the Tigers' eastern stronghold.
About 4,500 people have been killed since last year alone.
The government has vowed to destroy the Tigers militarily, while the separatists say they will step up attacks using a home-grown air force of light planes smuggled into the country in pieces.