COLOMBO (AFP) - Sri Lankas Tamil Tigers are slowly giving up their fight against advancing government troops, the islands military said Friday as it appeared poised to capture the last tiny strip of rebel territory. A military spokesman told AFP around 10,000 civilians had managed to flee to government areas, and that there was now hardly anybody left in the rebel zone on the northeast coast. They are slowly giving up. They are blowing up whatever arms and ammunition they have, Brigadier Udaya Nanayakkara said of the remnants of the once-powerful separatist army. The navy said it had captured the family of a top Tamil Tiger military commander Sea Tiger chief Colonel Soosai as they tried to escape by boat. But there was no sign of rebel chief Velupillai Prabhakaran. Meanwhile, the Sri Lankan government vowed Friday to capture all Tamil Tiger-held territory within 48 hours, despite international calls for a truce and accounts of a humanitarian catastrophe. The signal that a final push against the beleaguered separatist guerrillas was in full swing came as United Nations Secretary General Ban Ki-moons chief of staff was rushing to the island in a fresh effort to stop the carnage. The International Committee of the Red Cross (ICRC), the only neutral organisation working in the conflict area, said its staff were witnessing an unimaginable humanitarian catastrophe. Former colonial power Britain said it wanted an investigation into alleged war crimes, while the United States announced it was blocking a two-billion-dollar International Monetary Fund bailout package for Sri Lanka. Tens of thousands of Tamil civilians are believed to be trapped inside a tiny patch of jungle on the northeast coast still held by the rebels. Hundreds have been reported killed in indiscriminate shelling over the past week, adding to the thousands left dead since the rebels were pushed into a corner at the start of the year. Sri Lankan government spokesman Anusha Palpita said the war against the remaining rebels would be over by Sunday morning. The president (Mahinda Rajapakse) assured that within the next 48 hours the thousands of Tamil civilians will be freed from the clutches of the Tamil Tigers, Palpita said. All territory will be freed from Tiger control. We are closing in from all directions, military spokesman Brigadier Udaya Nanayakkara added. The government maintains that the Tigers are using civilians as human shields and they need to be rescued. Any civilian deaths inside Tiger territory have been blamed on the rebels. The UNs human rights chief Navi Pillay, however, has said both sides may be guilty of war crimes. The ICRC, the only aid organisation that the government allows to work in the conflict zone, said the situation was disastrous. Our staff are witnessing an unimaginable humanitarian catastrophe, ICRC director of operations Pierre Krahenbuhl said in Geneva, adding Red Cross staff had been unable to bring in food and pull out civilians for the past three days because of fierce fighting. A top UN envoy, the secretary generals chief of staff Vijay Nambiar, was meanwhile due on the island on Saturday to help resolve the humanitarian situation, officials in New York said. Prior peace missions by top diplomats have ended in failure, and on Thursday the Sri Lankan government which finally has the upper hand against the LTTE after more than three decades repeated it would not cave in to pressure. US Secretary of State Hillary Clinton said this meant it was not an appropriate time to consider a massive IMF bailout loan for the island. Sri Lankas central bank, however, brushed off the threat. In Britain, junior foreign minister Bill Rammell called for a war crimes probe something already demanded by leading human rights groups. The UNs estimate, if it is accurate, of over 6,500 civilian deaths since January is truly shocking and appalling, he said, stressing a need for a probe to determine whether war crimes have been committed.