The men were killed at Vandaramullai in the district of Batticaloa as army soldiers conducted an operation to clear the main road of mines planted by Tiger rebels, the official said.
The two men had lobbed a grenade at security forces when they were challenged, the official said, adding that a soldier had been wounded.
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The latest violence comes amid mounting tension in the neighbouring district of Trincomalee where six farmers from the majority Sinhalese community were shot dead late Sunday by suspected Tiger rebels.
A nighttime curfew in the area was lifted at dawn Monday, a local police official in Trincomalee said.
Attempts by peace broker Norway to get the government and Tamil rebels to resume ceasefire talks remain inconclusive.
The February 2002 ceasefire has come under renewed pressure after a spate of bomb attacks in the past two weeks.
At least 70 people have been killed in bombings alone while Tamil rebels say 70 civilians were slain by pro-government militia or by secu