"I suggest Sri Lanka tries to prepare negotiations to end the long rebellion in order to give peace a chance"
Mohamed Hassan, Galkayo, Somalia
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The statement also said he was killed inside rebel-held territory.
Udaya Nanayakkara, a spokesman for the defence ministry, confirmed to Al Jazeera that Thamilselvan had been killed in an operation at 6am.
Paikiasothy Saravanamattu, from the centre for policy alternatives in Colombo, told Al Jazeera that Thamilselvan's death would be a loss for the LTTE given his negotiating experience.
"He had the experience of being part of the negotiating team and dealing with the outside world on behalf of the LTTE. And in that sense it will certainly be a loss," he said.
Saravanamattu predicted the latest development would provoke a "hardening of positions" from both sides.
"Unless there is an outright victory for one side or the other or large international intervention there is not going to be a viable peace initiative anytime soon," he said.