The United Nations refugee agency estimated Tuesday that as many as 850 migrants had perished in a boat capsizing this week off the coast of Libya, as the ship’s captain and a crew member were taken into custody on criminal ­charges.

The U.N. estimate would confirm fears that the accident was the single worst disaster involving the flow of migrants seeking to reach Europe across the Mediterranean Sea.

But Italian prosecutors gave a broader range on the possible death toll, saying that interviews with survivors placed the number of victims between 400 and 950.

They said crew members from the Portuguese merchant vessel that had tried to aid the ship had estimated about 850 were aboard. Only 28 migrants survived.

A substantial number of passengers — including scores of women and children — perished Sunday as they were trapped below decks on the three-tiered vessel, apparently helpless as the boat tipped over, according to interviews with survivors.

Coupled with previous fatalities during the first half of the month, the estimate by the Office of the U.N. High Commissioner for Refugees would put the migrant death toll for April so far well over 1,000 — making it “the worst month ever recorded,” said Adrian Edwards, a spokesman for the refu­gee agency.

The prosecutor’s office said — according to witnesses — that the capsized ship left from somewhere near Tripoli on Thursday evening. The migrants had been kept — up to 30 days — inside a farm near the port and were loaded onto trucks in groups of 30 before they embarked. In at least one instance, one of the migrants was hit with a club because he wanted to go to the bathroom and did not ask for permission. Each passenger had to pay 500 to 1,000 Libyan dinars for the trip.

Prosecutors also offered more insight into what went wrong in the inky waters that night.

They said the capsizing appeared to be the product of two factors. The captain, they said, executed a faulty maneuver when attempting to steer toward the King Jacob, the Portuguese vessel whose crew was attempting a rescue, leading to a collision. At the same time, migrants shifted to one side of the overloaded boat, leading it to capsize.

With more migrants streaming toward Europe — including three more reported dead off the coast of Greece on Tuesday — aid agencies feared the numbers would yet rise.

Illegal migration into Europe

On Tuesday, the Italian coast guard launched a dawn rescue about 80 miles southeast of Calabria, saving 446 migrants aboard a fishing boat that was starting to sink. All passengers — including 59 children and 95 women — were taken aboard an Italian navy vessel.

In Sunday’s tragedy, Italian prosecutors said Mohammed Ali Malek, 27, the Tunisian captain, and Mahmud Bikhit, 25, a Syrian crew member, were taken into custody after a ship carrying survivors docked in Catania, Sicily.

Both men were charged with aiding and abetting illegal immigration. The captain was also charged with reckless multiple homicide and faulty handling of a vessel at sea.

Stephanie Kirchner in Berlin, Stefano Pitrelli in Treviso, Italy, and Brian Murphy in Washington contributed to this report.

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