Migrants believed to have started their journey in Tunisia, Italian officials say.
PM Mario Draghi wanted to propose at May 24 summit that EU make a deal with Libya to offer financial aid in exchange for hosting refugees, local media had reported.
The island's mayor appealed to the Italian government to deal with the issue after local media reported that many people took to sleeping on mattresses outdoors after the housing centre had filled up.
The woman was staying at a migrant holding centre designed to hold about 100 people but in recent days has been home to nearly 10 times as many due to a pickup in arrivals.
The boat, which survivors said had departed from Libya taking advantage of a respite in bad weather, was believed to be carrying some 170 people.
The Italian Coast Guard said those rescued, who included three children and 13 women, were brought to the port of Lampedusa.
Italian coastguard says it recovered bodies of 13 women, some of them pregnant, after a small overloaded boat carrying around 50 migrants capsized off Lampedusa.
The move comes after Spanish navy set sail in an attempt to save migrants stuck in the boat off the coast of Italy.
The French decision comes after the charity boat, which is currently in limbo off the coast of Italian island of Lampedusa, refused to take Spain's offer to dock citing an emergency situation.
The sailboat Alex, carrying 41 migrants, declined a Maltese offer to go to Malta, as the Mediterranea NGO operating it said such a long journey would have been dangerous for the people aboard.
Far-right League leader Matteo Salvini has tried to ban the Dutch-flagged vessel from approaching under a "closed ports" policy, which has seen migrants repeatedly stranded at sea.
Fishermen in the Tunisian town of Zarzis have been frontline actors in saving migrant lives at sea even though their humanitarian assistance is increasingly being compromised by hostile European migration policies.
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