ROME, April 20 (Reuters) - Up to 500 migrants might have drowned in the Mediterranean last week when human traffickers crammed people onto an already overcrowded ship, causing it to sink, the U.N. refugee agency said on Wednesday.

Somalia's government said on Monday about 200 or more Somalis may have died in the tragedy while trying to cross illegally to Europe. After talking to survivors, the UNHCR agency said the overall death toll might have been much higher.

"If confirmed, as many as 500 people may have lost their lives when a large ship went down in the Mediterranean Sea at an unknown location between Libya and Italy," the UNHCR said.

The agency said the survivors - 37 men, three women and a three-year-old child - were rescued by a merchant ship and taken to Greece on April 16.

They recounted that they had been among 100 to 200 people who set sail from Libya last week headed for Italy. After several hours at sea, the traffickers tried to move them onto a bigger ship that was already packed with migrants.

This ship sank before the survivors could board it. They then drifted at sea for up to three days before being saved. The group was made up of 23 Somalis, 11 Ethiopians, six Egyptians and one Sudanese national.

The Somali government said on Monday that the capsized boat had set sail from Egypt.

News of the disaster emerged on the first anniversary of one of the worst disasters in the Mediterranean in recent times, when an estimated 800 migrants drowned off the Libyan coast after the fishing boat they were sailing in collided with a mercantile vessel that had been attempting to rescue them.

Some 150,000 migrants reached Italy by boat in 2015, the vast majority sailing from Libya. So far this year, about 25,000 migrants have arrived, an increase of 4.7 percent over the same period last year, according to Interior Ministry data. (Reporting by Crispian Balmer; Editing by Tom Heneghan)