"We suffered 11 soldiers killed and 20 wounded and the terrorists lost seven killed and 27 wounded," a government spokesman said.
The fighting had subsided by Saturday morning, he said.
The latest clash came as Sri Lanka prepared to stage a two-day summit of the eight-member South Asian Association for Regional Co-operation (Saarc).
Manmohan Singh, India's prime minister, was among the first to arrive for the meeting. He was followed soon after by Yousaf Raza Gilani, his Pakistani counterpart.
Heavy security
Colombo, which believes it has the upper hand in the conflict after driving the rebels from their eastern stronghold, has sharply beefed up security in and around the capital of 650,000 residents.
Minelle Fernandez, Al Jazeera's correspondent in Colombo, said the Sri Lankan government was taking no risks "even though the LTTE declared a unilateral ceasefire over a week ago in light of the summit and they said that they wish the summit the best success".
"In fact, security within the capital and around the capital is very heavy. All eight leaders have arrived with heavy security back up," she said.
The fighting is taking place 250km to the north, but there has recently been a string of deadly attacks on the capital that the government has blamed on the rebels.
In late July, the LTTE offered a unilateral ceasefire for the summit, but Colombo brushed off the proposal and stepped up attacks against rebel positions in the north.
The Tigers are fighting for a separate Tamil homeland in the majority Sinhalese nation.
The defence ministry said helicopter gunships were deployed to provide cover for ground troops engaged in Friday's battle.
The Tamil Tigers said they had resisted a major military onslaught and claimed killing 30 soldiers and wounding another 60. The rebels did not give their casualties.
The pro-rebel Tamilnet.com website said the Tigers had also seized a troop carrier that was trying to evacuate wounded soldiers.