COLOMBO, Sri Lanka - Some 35,000 civilians fled the last corner of Sri Lankan territory held by the Tamil Tigers, the military said Monday, as the government warned the rebels it would launch a final assault in 24 hours.

The air force showed reporters footage taken by a surveillance plane in which scores of civilians ran toward the military's defence line, most of them carrying just a few possessions in bags on their heads.

President Mahinda Rajapaksa said in a televised speech that the operation was the "largest-ever hostage rescue mission in history."

He said the military rescued the noncombatants by opening several routes into the war zone. But a pro-rebel website said hundreds of civilians were feared killed in the "total chaos" that prevailed when the soldiers entered the zone.

It is not possible to verify any of the claims because the war zone is restricted to journalists.

Military spokesman Brig. Udaya Nanayakkara said soldiers advanced into the zone and seized a fortification built by the rebels before rescuing the civilians.

The exodus comes just days after the military imposed a unilateral two-day ceasefire to encourage civilians to flee. Only a few hundred left at that time, prompting the government to renew accusations that the rebels are holding civilians against their will to use as human shields.

The charge has also been levied by aid groups, though the rebels have denied it. It was not possible to contact the rebels for comment.

The United Nations says an estimated 100,000 civilians are trapped in the a war zone measuring just 20 square kilometres. The UN also estimates that some 4,500 noncombatants have been killed in the last three months amid fierce fighting.

The UN and others have called for a negotiated ceasefire to allow the civilians to leave. The government has rejected such calls, saying it's on the verge of crushing the 25-year insurgency.

The government said Monday that rebel leader Velupillai Prabhakaran and his fighters have 24 hours to surrender before a final assault - one of many such promises that troops will soon end the conflict.

Defence spokesman Keheliya Rambukwella said the government's preferred option is to catch Prabhakaran alive and said the ultimatum was a final opportunity for the leader to end the conflict.

The rebels have refused previous calls for their surrender.

Rambukwella said the rebel leader's capture or death has now become "inevitable" because he will soon lose his civilian cover.

"He (Prabhakaran) doesn't have that option now," Rambukwella said. "Our first option is to capture him and bring him before the law."

In recent months the military has ousted the Tamil rebels from all their strongholds in an all-out offensive, forcing the rebels to retreat to the "no-fire" zone for a final stand.

The rebels have been fighting to create an independent homeland for ethnic minority Tamils, who have faced decades of marginalization by successive governments controlled by ethnic Sinhalese. More than 70,000 people have been killed in the violence.