The ethnic separatist conflict has claimed at least 60,000 lives since it began in 1972.
The three Tamils working for the Mitsui cement company died in Trincomalee district, police said, adding that the triple murder was under investigation.
In the neighbouring district of Batticaloa, troops and the rebel Liberation Tigers of Tamil Eelam (LTTE) exchanged artillery and mortars, military officials said.
There were no immediate reports of casualties from the shelling, which came ahead of an annual policy statement that Tiger supremo Velupillai Prabhakaran was due to deliver in the early evening.
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Meanwhile, the defence ministry accused the LTTE of mining the main land access to the rebel-held Vakarai area in Batticaloa district to block supplies of essential food and medicines.
The allegation could not be verified independently.
Fighting has escalated in tit-for-tat battles that have officially claimed 3,422 lives this year and frustrated efforts by Norway to revive a 2002 ceasefire agreeme