Rasiah Ilanthirayan, a Tiger spokesman, said by email that the Tigers thwarted a two-pronged attempt by government troops to advance near their fortifications, backed by artillery and mortars.
Ilanthirayan did not give casualty figures for the Tigers but said that sixteen soldiers were killed and 45 were wounded in the battle.
The clash in the north came days after government troops captured the last Tiger stronghold in Sri Lanka's east, the scene of heavy fighting over the last few weeks.
The government victory on Wednesday over Thoppigala - the last organised Tiger resistance area in Eastern Province - has given the government total control of the province for the first time in 13 years.
The rebels, who still maintain a de facto state in parts of the north, vowed to hit nationwide military and economic targets in revenge.
Meanwhile, hundreds of Buddhist monks paraded through Colombo offering blessings to government forces for Wednesday's victory.
Athuraliye Rathana, one of the monks, said: "We urge the government to continue this victory march as we can achieve a genuine and lasting peace only by completely defeating terrorism."
The Tigers have been fighting since 1983 for a separate homeland for Sri Lanka's Tamil minority, a predominantly Hindu group that has faced decades of discrimination by the majority Sinhalese, who are predominantly Buddhist and dominate the government and military.
About 70,000 people have been killed in more than two decades of fighting.
Also on Saturday, police said they found 784 sticks of gelignite explosives hidden in a truck that they stopped at a checkpoint in Galewela town, 130km northeast of Colombo, the capital.
The truck's driver and another man were arrested.
It was not immediately known whether the explosives were intended for the Tamil Tigers.