COLOMBO, Sri Lanka - Thousands of civilians braved rebel fire Thursday to break out of Sri Lanka's war zone, the military said, as health workers abandoned the only hospital in the area -- leaving hundreds of wounded behind -- because of unrelenting shelling.

At least four civilians were killed and 14 others wounded when the rebels shot at them as they waded across a lagoon that forms the front line of the war, the military said.

The Red Cross said the war zone was wracked by fighting Thursday, despite appeals from President Barack Obama and the U.N. for the two sides to end their civil war and let the estimated 50,000 civilians trapped in the area escape.

The government has cornered the Tamil Tigers on a tiny strip of land -- bordered by the sea on one side and a vast lagoon on another -- and vowed to finish off the rebels after 25 years of civil war.

It has denied it is responsible for the shelling that has killed hundreds of civilians, saying the military has not fired heavy weapons in the area in weeks.

The U.S.-based group Human Rights Watch, however, says satellite images and witness testimony contradict that claim and has accused both sides of using civilians in the tiny pocket of land as "cannon fodder."

As the military pressed ahead with its offensive, 2,700 civilians waded across the lagoon and into government-controlled territory under a hail of rebel gunfire, military spokesman Brig. Udaya Nanayakkara said. Another 2,000 civilians were waiting on the far shore to escape, 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 most journalists and aid workers from the conflict zone.

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

The war zone has been pounded by incessant shelling over the past six days that health officials say has killed hundreds of civilians, including about 100 people killed in two strikes on the makeshift hospital.

Though the number of wounded was rapidly increasing, doctors and aides abandoned the facility because heavy 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 in the facility Thursday in desperate need of treatment, along with more than 100 bodies waiting to be buried, the official said. Many other wounded civilians fled after the hospital was shelled Wednesday for second time in two days, he said.

The medical staff had huddled in a nearby bunker for more than 24 hours by Thursday evening and tried to ignore the cries off patients begging for food and water, 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, said Sarasi Wijeratne, spokeswoman for the International Committee of the Red Cross.

"The situation is becoming desperate because of the fighting, which is intense and uninterrupted," she said.

With the death toll mounting, Obama on Wednesday demanded the rebels lay down their arms and release those trapped. He also admonished the government to stop firing artillery into the war zone.

"Now's the time, I believe, to put aside some of the political issues that are involved and to put the lives of the men and women and children who are innocently caught in the crossfire, to put them first," Obama said in Washington.

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

Both sides welcomed Obama's appeal for an end to the civil war, but ignored his criticism of their conduct.

Sri Lankan Foreign Secretary Palitha Kohona said the government was "extremely reassured" by Obama's call for the rebels to lay down their weapons and release the civilians, and he denied the government was firing artillery into the densely packed war zone.

The rebels' political chief, Balasingham Nadesan, praised Obama in a statement e-mailed to The Associated Press "for passionately talking about the plight of Tamil civilians and calling for urgent actions to alleviate the mounting humanitarian crisis."

The rebels did not address his call for their surrender.