Four previous peace attempts ended in failure.
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The powerful blast went off in the Jaffna peninsula while troops were on a cordon-and-search operation, the defence ministry said in a statement, adding that one soldier was wounded.
Another soldier and a civilian were wounded when the Tigers opened fire on an army foot patrol in a separate incident, the ministry said.
The skirmishes came as peace broker Norway tried to cement face-to-face talks between the Sri Lankan government and the rebel Liberation Tigers of Tamil Eelam (LTTE) in Switzerland starting October 28.
At least 250 people were killed in Sri Lanka last week in two suicide attacks and other violence across the island.
Amid the spiralling bloodshed, the island's donors have mounted pressure on both sides to end an eight-month deadlock in the peace process and revive a 2002 ceasefire that has been left in tatters by the violence.
More than 60,000 people have been killed in the island's drawn-out Tamil separatist conflict.