Soldiers backed by tanks and air cover were battling to establish full control over the 30-kilometre (18 mile) stretch of coast, Brigadier Nandana Udawatte told an AFP reporter on the scene.
"We are moving along the coast as well as to the north-west towards another pocket of Tiger resistance," he told journalists flown to Kumalamunai, a small settlement just south of Mullaittivu town that was captured Sunday.
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The military planned to take journalists by road to Mullaittivu later Tuesday to highlight their success in driving the Liberation Tigers of Tamil Eelam (LTTE) out of their military headquarters.
Udawatte said his troops had killed at least 2,000 Tamil Tiger rebels and wounded nearly 3,000 in the year-long battle to capture Mullaittivu.
The brigadier said the rebels had established three defence lines to protect Mullaittivu, but his men had surprised them by crossing a lagoon by boat.
"We also suffered casualties in overcoming their obstructions," he said.
"They had