Vanniasingham Vigneswaran, who spearheaded the Tamil Resurgence Movement in Trincomalee, was gunned down near the port town's main bank in the morning.
His movement had often clashed with the Sinhalese majority groups in Trincomalee where he opposed the erection of a Buddhist statue last year.
Police in the multi-ethnic town said investigations were at a very early stage and it was unclear who carried out the attack.
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The two Muslims serving in the police "homeguard" unit died as they returned home after a night shift at Welikanda, 250 kilometres (150 miles) northeast of the capital Colombo.
Defence Ministry spokesman Brigadier Prasad Samarasinghe pointed a finger at the separatist Liberation Tigers of Tamil Eelam (LTTE) for the killings.
"The shooting has taken place in an area frequented by the Tigers", Samarasinghe said.
Other Tamil paramilitary forces also operate in the area, which government security forces patrol and is a hotbed of violence.
The killings came a day aft