A total of 103 bodies have been recovered and more have been found inside the wreck, coast guards say.
Passengers reportedly threw themselves into the sea when a fire broke out on board. More than 150 of the migrants have been rescued.
Most of those on board were from Eritrea and Somalia, said the UN.
The boat was believed to have been carrying up to 500 people at the time and some 200 of them are unaccounted for.
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Alan JohnstonBBC News, Rome
This marked a tragic end to a long journey from countries as far as Eritrea and Somalia.
Over the years there have been numerous disasters involving migrants off Lampedusa, but seldom on anything like this scale. The island’s mayor wept as she took in the scene on the harbour wall.
Furious demands are being made for an end to the dangerous trafficking of people across the Mediterranean. But it is hard to see how the flow could be curbed, with so many people so desperate for a chance to make a new life in Europe, and traffickers in so many ports ready to take their money.
Italian Interior Minister Angelino Alfano said the ship had come from Misrata in Libya and began taking on water when its motor stopped working.
It is thought that some of those on board set fire to a piece of material to try to attract the attention of passing ships, only to have the fire spread to the rest of the boat.
Simona Moscarelli, a spokeswoman from the International Organization for Migration in Rome, told the BBC that in order to escape the fire, “the migrants moved, all of them, to one side of the boat which capsized”.
She estimated that only six of about 100 women on board survived, adding that most of the migrants were unable to swim.
“Only the strongest survived,” she said.
It is one of the worst such disasters to occur off the Italian coast in recent years; Prime Minister Enrico Letta tweeted that it was “an immense tragedy”. The government has declared a day of national mourning on Friday.
“There is no miraculous solution to the migrant exodus issue,” said Italian Foreign Minister Emma Bonino. “If there were we would have found it and put it into action.”
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Without the necessary paperwork, the only way for migrants to get to Europe is to put themselves in the hands of criminal gangs”
image of Andrew HardingAndrew HardingAfrica correspondent
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In a separate incident on Thursday, local media reported that around 200 migrants were escorted to the port of Syracuse on the island of Sicily, when their vessel encountered difficulties five miles off the coast.
Earlier this week, 13 migrants drowned while trying to reach Sicily.
‘Continuous horror’Footage from Lampedusa showed bodies being laid out on the dockside.
The mayor, Giusi Nicolini, described the scene as a “continuous horror”.
“It’s horrific, like a cemetery, they are still bringing them out,” she said, according to Reuters.
BBC News, Rome.
The Question is How we can stop such disaster like that with the Corruption of the United Nation HigH Commissioner For Refugees,Particularly office in New Delhi-India and Somali Refugees are dying for Starvation in India last One Decide without reporting to the World.
“We need Action not Cheap words”.