Only 28 people survived the capsize, UNHCR spokesperson Carlotta Sami told the Skytg24 news channel in Italy. The survivors indicated there had been more than 700 on board, she said.
The Maltese navy put the numbers on board at around 650 and said an alert had come in around midnight on Saturday.
"We have deployed our assets along with others from Italy and we are assisting in the rescue operation," a Maltese navy spokesperson told AFP on Sunday without giving any other details.
If confirmed, the tragedy would be by far the biggest in a growing catalogue of mass drownings of migrants attempting to reach the European Union on overcrowded, unseaworthy boats run by people smugglers.
The boat went down about 60 miles off the Libyan coast and 120 miles south of the Italian island of Lampedusa.
The disaster comes after a week in which two other shipwrecks left an estimated 450 people dead. More than 11,000 other would-be immigrants to Europe have been rescued by Italy's coastguard and other boats.
Some 1,500 migrants have now drowned in the waters between Libya and Italy since the start of the year.
Aid organisations have called for a concerted international effort to put better search-and-rescue systems in place and for action to stem the unprecedented numbers of asylum seekers and migrants from Asia, the Middle East and Africa seeking to reach Europe.
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