Government troops have confined Liberation Tigers of Tamil Eelam (LTTE) fighters to an area of 21 square kilometres (eight square miles), most of which is a government-declared safe zone, the minister said.
"Therefore, it is apparent that the LTTE are now at the imminent brink of defeat," said Keheliya Rambukwella, minister for foreign employment and the government's defence spokesman.
At the height of their power in the mid-1990s, the Tigers controlled more than two-thirds of the island's coastline and one third of the total land mass.
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The collapse of the Tigers began two years ago, and accelerated after the government pulled out of a Norwegian-brokered truce in January 2008.
Earlier this year, the military seized the political and military headquarters of the Tigers and vowed to completely defeat the rebels by next month, a victory that would end one of the world's longest-running civil wars.
There was no immediate word from the Tigers, who have been fighting to carve o