* At least 62,000 flee, military says
* Tigers vow no surrender
* Tiger leader in war zone - Tigers
* Red Cross warns of catastrophe
(Updates number fleeing)
By C. Bryson Hull and Ranga Sirilal
COLOMBO, April 21 (Reuters) - Sri Lankan soldiers battled into the last redoubt of the Tamil Tigers on Tuesday, and an exodus of people trapped by the rebels in the coastal strip hit more than 62,000, the military said.
The International Committee of the Red Cross (ICRC) warned the situation was "nothing short of catastrophic" and urged both sides to prevent further mass casualties among civilians, saying hundreds had been killed in the past 48 hours.
The neutral agency did not assign blame to either side.
The operation gathered speed after the military's noon (0630 GMT) deadline for the Liberation Tigers of Tamil Eelam (LTTE) to surrender passed without any word from the separatists, in what appears to be the final act in Asia's longest-running war.
The LTTE hours later vowed no surrender, despite being massively outgunned by a military built up to wipe them out and finish a conflict that has percolated since the early 1970s but erupted into full-blown civil war in 1983.
"LTTE will never surrender and we will fight and we have the confidence that we will win with the help of the Tamil people," Seevaratnam Puleedevan, secretary-general of the LTTE peace secretariat, told Reuters by telephone.
Sri Lanka's military, in what it dubbed the world's largest hostage rescue operation, moved in to keep the stream of people moving and give troops a clear shot at the LTTE and its elusive leader Vellupillai Prabhakaran.
"So far 62,600 people have come out and still they are coming," military spokesman Udaya Nanayakkara said. Earlier, he said soldiers had reached the beach, which meant they had divided the Tigers' last remaining area into two.
He denied civilians were being harmed.
The Tigers' Puleedevan said Prabhakaran, the 54-year-old guerrilla who since the 1970s has single-mindedly led a fight for a separate nation for Tamils, was directing the fight in what the army set up as a no-fire zone, but is now a last battleground. [ID:nCOL472502].
A BLOODY END?
After the conventional end of the war, Sri Lanka will face the challenges of healing divisions between the Tamil minority and Sinhalese majority, and boosting a $40 billion economy suffering on many fronts including a weakening rupee LKR=.
But on Tuesday for the second day running, the Colombo Stock Exchange .CSE gained on positive investor sentiment over the war effort and was at a more than two-month high.
Sri Lanka is seeking a $1.9 billion International Monetary Fund loan to ease a balance of payments crisis and boost flagging foreign exchange reserves, which Central Bank Governor Ajith Nivard Cabraal said should be finished soon. [ID:nSP402337]
The United Nations and Western governments have urged the military to renew a brief truce to negotiate the civilians' exit, a plea the government has rejected on the grounds the Tigers have dismissed all entreaties to let the people out.
Sri Lankan President Mahinda Rajapaksa again turned down Britain's attempt to send a special envoy and ruled out any pause in military action during a phone call with Prime Minister Gordon Brown on Monday, the president's office said.
"President Rajapaksa observed that this movement of civilians had evoked a completely new situation and he had instructed that additional consignments of food, medicine and other essentials be dispatched," a statement on Tuesday said.
Puleedevan, the LTTE peace secretariat head, again urged a permanent ceasefire and accused the government of killing 1,000 people and wounding 2,000 on Monday via shelling.
The government has denied that and accuses the Tigers of creating a humanitarian crisis to build international pressure for a ceasefire to try and rearm, as they have done in the past.
The Red Cross said it feared the operation could lead to a drastic increase in the number of casualties.
"The situation is nothing short of catastrophic. Ongoing fighting has killed or wounded hundreds of civilians who have only minimal access to medical care," ICRC operations director Pierre Kraehenbuehl said in a statement.
At least 50,000 people remain inside the one-time no-fire zone, ICRC spokesman Simon Schorno said in Geneva. The military said the number is less than that but it has no updated figure. Before the exodus, it had said around 60,000 were there.
The stream of people leaving started on Monday after troops breached an earthen rampart blocking the main route out of the 17 square km (6.5 sq mile) zone.
The final operation to crush the Tigers set off protests by expatriate Tamils in London and Paris, the latest in weeks of demonstrations against the offensive in cities across the world.
In Paris, around 180 people were arrested and four injured when a demonstration turned violent as protesters blocked an intersection and threw objects at buses and police, police said.
The United Nations has long said the LTTE was forcibly preventing people from leaving and making others fight, which the LTTE denies.
Sri Lanka provided video taken from unmanned aerial drones on Monday showing thousands of people fleeing the area, and what it said were LTTE fighters firing at others trying to get out.
It was impossible to independently verify the competing accounts since the battle zone is off-limits to most outsiders.
(Additional reporting by Shihar Aneez, the Paris bureau, and Stephanie Nebehay in Geneva; Writing by Bryson Hull; Editing by Mark Trevelyan) (For a related graphic see here. jpg )