Around 12,000 migrants have arrived at reception centres in Malta and Italy. An estimated 1,200 are missing and presumed dead, adding a further human tragedy to the thousands killed in three months of fighting to topple leader Muammar Gaddafi.
"It is estimated they have got a one in 10 chance of perishing during that journey" across the Mediterranean, Melissa Fleming, chief spokeswoman for the U.N. High Commissioner for Refugees (UNHCR), told a Geneva news briefing.
In a UNHCR camp in Tunisia, agency workers interviewed three Ethiopian men who said they were among nine survivors from a boat that left Tripoli on March 25 carrying 72 people.
The boat is believed to be one that was the subject of a British newspaper report, which prompted NATO to say on Monday it was investigating the claim it had not gone to the aid of a vessel even though it had made contact with a NATO warship.
One of the Ethiopians interviewed said the boat ran out of fuel, water and food, then drifted for more than two weeks before reaching a beach back in Libya.
Military vessels had twice passed the 12-metre-long (12-yard-long) boat, crowded to the point there was barely standing room, without stopping, he said.
The first boat refused a request to board and the second just took photos, although he could not say where the vessels had come from.
"According to the refugees, when water ran out people drank sea water and their own urine. They ate toothpaste. One by one people started to die," Fleming said, adding that after waiting a day or so, they decided they had to drop the bodies into the sea.
The boat was among many believed to have left Libya without a captain, leaving the migrants to do the navigation themselves.
"I have heard accounts that perhaps there has been a captain for the first 100 metres or so and then a small boat will take the captain back to shore. They provide the passengers with a compass and say 'Lampedusa is in that direction. Best of luck'," said Fleming, referring to the small southern Italian island where many refugees have headed.
It eventually reached shore on a beach near Zliten, between Tripoli and the Tunisian border where one woman died on the beach from exhaustion.
Ten suriving men walked to the town of Zliten, where they were arrested, taken to a hospital and then a prison, where another survivor died.
They were released from jail after Ethiopian friends in Tripoli paid the prison $900. The survivors said they had also paid the smugglers $800 to make the journey that cost so many their lives.
Some 750,000 people have fled Libya over land to neighbouring Egypt and Tunisia, which have borne the brunt of the crisis, according to the UNHCR.
Thousands of displaced people now need a home and it appealed to Western countries with capacity and space to accept more refugees for resettlement.
"Only one percent of people who have left Libya have made it to Europe, so we're calling on European governments to show some solidarity," Fleming said.