Tamil Tigers on Friday were on the verge of total collapse with just a kiolmetre separating two Sri Lankan Army divisions from overrunning the entire coastal area held by them, even as the families of LTTE leaders began to flee the war zone.

With the Lankan offensive appeared reaching its conclusion, more than 10,000 trapped Tamil civilians fled the last remaining area held by the LTTE as President Mahinda Rajapaksa vowed to stamp out the rebels within the next 48 hours.

In another big blow to the LTTE, which has been plagued with desertions by senior leaders, family members of LTTE's naval wing chief Colonel Soosai, including his wife, were captured by the Sri Lankan Navy as they tried to flee the island in a boat.

Soosai, the chief of 'Sea Tigers', is a close confidant of Velupillai Prabhakaran and said to be the senior most leader in the military wing after the LTTE supremo.

Two top LTTE leaders -- Daya Master and George -- gave themselves up before the Sri Lankan Army last month, while a top military aide of Prabhakaran is believed to have been killed in the intense fighting.

Military spokesman Brig Udaya Nanayakkara said the "rebels are slowly giving up. They are blowing whatever arms and ammunition they have."