Sri Lanka's military says the eldest son of the top Tamil Tiger rebel leader has been killed in fighting.

Military spokesman Udaya Nanayakkara said army troops on Monday found the body of Charles Anthony, the son of Velupillai Prabhakaran.

Prabhakaran has three children and Charles Anthony — named after a rebel leader who died earlier in the war — was the only one thought to be fighting along with his father.

There was no immediate comment from the rebels and it was not possible to independently verify the military's claim as journalists and observers are barred from the war zone.

On Sunday, a rebel spokesman said the Tamil Tigers are willing to lay down their weapons after being defeated by a major government offensive along Sri Lanka's northeast coast.

Selvarasa Pathmanathan, a senior member of the Liberation Tigers of Tamil Eelam (LTTE), said the group has no option left to protect civilians in the area but to stop fighting.

The Tamil Tigers have "decided to silence our guns," he said in a statement appearing on a pro-LTTE website.

He also also urged the government to withdraw its forces and hold peace talks.

President Mahinda Rajapaksa declared victory over the Tamil Tigers on Saturday after government forces surrounded the remaining separatist rebels in a tiny patch of land no larger than one square kilometre.

The government also rejected the last-ditch call for a ceasefire, saying the thousands of civilians trapped in the war zone all have escaped to safety and there was no longer any reason to stop the battle.

Reports that civilians have left the battle zone cannot be independently verified because journalists and aid workers are still barred from the area.

The military said the remaining guerrillas were still fighting. It reported that rebel suicide bombers had blown themselves up on the front line on Sunday morning, and more than 70 were killed trying to flee overnight.

With a war that has killed well over 70,000 people nearing its end, Sri Lankans poured into the streets in spontaneous celebration.

Rajapaksa scheduled a nationally televised news conference for Tuesday morning in parliament, where he was expected to tell the country the war was over.

The fate of the Tamil Tigers' top commanders remained unclear, including the whereabouts of Prabhakaran.

With files from The Associated Press