The clash erupted as government soldiers tried to destroy rebel mortar positions east of Madhu village in Mannar district, from where the Tigers have frequently launched attacks on military defense lines, the Defense Ministry's information center said.
The center said about 20 Tamil rebels and two soldiers were killed in the battle.
Rebel officials could not be reached for comment and independent verification of the details was not possible.
Also Wednesday, a roadside bomb targeting a foot patrol exploded in the east, killing two village guards and wounding three police commandos, the military said, blaming the rebels for the blast.
The violence come a day after Tamil Tiger planes bombed government positions in northern Sri Lanka in their second airstrike in more than two decades of war.
The insurgents claimed two airplanes carried out Tuesday's raid on the government's strategic Palaly military base in Jaffna peninsula.
The military, however, said only one aircraft was involved in the attack and that it was turned back before reaching the base. Six soldiers were killed in the air and artillery attack.
It was only the second rebel airstrike since the rebels started their campaign to create an independent homeland for ethnic minority Tamils in 1983.
The first, last month, killed three airmen and wounded 16 at an air force base outside the capital, Colombo.
On Monday, Sri Lankan officials ordered Norway's ambassador, who is trying to mediate a resumption of peace negotiations, to cancel a trip to the Tamil Tiger rebels' northern strongholds for security reasons.
A cease-fire mediated by Norway in 2002 brought a semblance of peace for a few years, but violence over the past 18 months has killed at least 4,000 people, taking the death toll in more than two decades of war to over 69,000.