Brigadier Prasad Samarasinghe, a military spokesman said: "When we were clearing an area ... two terrorists tried to attack our troops."
Government troops fired at the alleged attackers, killing both of them during the incident in Batticaloa on Monday, he said.
During a Christmas service on Sunday in the same city, unidentified armed men shot and killed Joseph Pararajasingham, 71, a pro-rebel parliamentarian.
Batticaloa has been the site of frequent skirmishes between rebel factions since the separatist movement split in 2004.
The government and the rebels have blamed each other for the assassination of the politician. The rebels want to create a separate homeland for Sri Lanka's 3.2 million ethnic Tamils in the northeast.
Also on Monday, a suspected rebel fatally shot Veerappan Thripupathy, 52, a member of a Tamil political group opposed to the Tamil Tigers in the northern town of Vavuniya, police officer L Bandara said. The group gave up arms in 1987 and joined Sri Lanka's political mainstream.
Tamil Tiger rebels want a separate
homeland for ethnic Tamils
The deaths followed the overnight killing of two suspected Sri Lankan army informers in the northeastern town of Trincomalee.
Trincomalee, Batticaloa and Vavuniya fall within the rebels' envisaged homeland that they have been trying to create since 1983.
The two alleged informers - both scooter rickshaw drivers - were killed by suspected rebels for passing information to the military, a police official in the port city said.
Batticaloa was the scene of several battles between the rebels after a powerful eastern commander and his followers split from the main Tamil Tigers group.
The uprising was ruthlessly suppressed by the main rebel group, but sympathy for the breakaway leader - known as Karuna - remains strong among Tamils in the east.
The Tigers also accuse the Sri Lankan military of backing Karuna's faction, an accusation the military denies.
Violence has also increased in Sri Lanka's ethnic Tamil-majority north and parts of the east since Velupillai Prabhakaran, the mainstream rebel leader, threatened to resume his struggle for an independent Tamil homeland if the government fails to address Tamils' grievances.
The Tamil Tigers started fighting in 1983 for a separate homeland in the island nation's north and east, claiming discrimination by the majority Sinhalese. The conflict has so far killed about 65,000 people.