Krishnasami Naguleswaran, 40, was shot dead in front of his house in Mannar on Wednesday night.
The former cadre of the Liberation Tigers of Tamil Eelam (LTTE) had undergone the Sri Lankan government's rehabilitation programme.
Police claimed to have recovered the gun used in the murder of Naguleswaran, who worked as as a brick-maker.
"We have found the T56 weapon used for the murder. We suspect it was due to a private grudge", said acting police spokesman Ruwan Gunasekera.
Sri Lanka government troops and the LTTE were locked in a nearly-three decade bloody war that ended in 2009 with the defeat of the Tamil Tigers following the death of its chief Velupillai Prabhakaran.
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