Thousands of civilians waded across a vast lagoon under a hail of rebel gunfire Thursday, breaking out of Sri Lanka's war zone in a mass exodus that left four civilians dead from Tamil Tiger bullets, the military said.

In the tiny coastal strip they had just fled, unrelenting shelling forced health workers to abandon the only hospital in the area, leaving hundreds of wounded patients begging for food and water, according to a health official in the war zone.

The Red Cross called the fate of the wounded "an unimaginable humanitarian catastrophe."

The government, which denies shelling the area, has cornered the Tamil Tigers on a spit squeezed between the sea and a lagoon and vowed to finish off the rebels after 25 years of civil war. The rebels, who demand a homeland for the ethnic Tamil minority, once controlled a shadow state across the north.

As the military pressed ahead with its offensive, 2,700 civilians braved rebel gunfire and waded across the lagoon into government-controlled territory, military spokesman Brig. Udaya Nanayakkara said. Another 2,000 civilians were waiting on the far shore to escape, he said. In addition to the dead, 14 people were wounded by rebel gunfire, he said.

The rebels have denied accusations they were holding the civilians as human shields and shooting at those trying to flee. Reports of the fighting are difficult to verify because the government has barred journalists and most aid workers from the conflict zone.

Nearly 200,000 civilians have escaped the war zone in recent months and are being held in overwhelmed displacement camps. The government has called on the estimated 50,000 people still trapped by the fighting to follow their lead, saying that only their presence is preventing the military from wiping out the rebels.

The U.N. said last month that nearly 6,500 civilians were killed in three months of fighting this year. Incessant shelling in the war zone over the past six days has killed hundreds more, including about 100 civilians who died in two strikes on the makeshift hospital, health officials said.

Though the number of wounded was rapidly increasing, doctors and aides abandoned the facility because the shelling made it too risky to work there, according to a health official in the war zone who spoke on condition of anonymity because he was not authorized to talk to the media.

About 400 badly wounded patients remained inside Thursday in desperate need of treatment, along with more than 100 bodies waiting to be buried, the official said. Many other wounded civilians fled the hospital for safety as well.

The medical staff huddled in a nearby bunker and tried to ignore the cries of patients begging for help, he said.

A Red Cross ferry attempting to deliver desperately needed food aid and evacuate the wounded had to turn back for the third day Thursday because of the violence.

"Our staff are witnessing an unimaginable humanitarian catastrophe," said Pierre Krahenbuhl, the International Committee of the Red Cross' director of operations. "No humanitarian organization can help them in the current circumstances. People are left to their own devices."

The Red Cross said the trapped civilians inside the war zone were taking cover in bunkers they had dug in the ground and were finding it even more difficult to get scarce drinking water and food.

"We need security and unimpeded access now in order to save hundreds of lives," he said in a statement from Geneva.

President Barack Obama on Wednesday demanded the rebels lay down their arms and release the civilians. He also admonished the government to stop firing artillery.

The U.N. Security Council issued similar demands to both sides and expressed grave concern at the worsening humanitarian crisis.

Both sides brushed off the criticism.

Secretary-General Ban Ki-moon's chief of staff, Vijay Nambiar, would leave for Sri Lanka later Thursday to underscore his plea for an end to the conflict without further bloodshed, U.N. deputy spokeswoman Marie Okabe said.