The Tigers have been driven back into just 73 square kilometres (28 square miles) of jungle, military spokesman Udaya Nanayakkara said, having controlled large swathes of the north and the east of the island less than two years ago.
Officials say the rebels are increasingly desperate and may launch more attacks such as the air strike on the capital Colombo on Friday, when two light aircraft were used in suicide missions that killed two people.
The UN's top humanitarian relief official, John Holmes, appealed to the government and the rebels to spare non-combatants as the warring factions appeared set for a final showdown.
Holmes said civilians were dying every day inside the war zone, where government troops are fighting to crush the Tigers' decades-long armed campaign for an independent Tamil homeland.
"I urge both sides to do everything they can for a peaceful and orderly end to avoid a final bloody battle," he said on Saturday at the end of his three-day visit to Sri Lanka.