PM Enrico Letta made the announcement during a visit to the island with European Commission President Jose Manuel Barroso.
Jose Manuel Barroso pledged 30 million euros ($40 million) of EU funds to help refugees in Italy.
At least 274 people, mostly from Eritrea and Somalia, died in the wreck.
Of more than 500 people on board, only 155 have survived. Divers are recovering bodies.
It is one of Italy’s worst disasters involving a boat carrying Europe-bound migrants from Africa.
Lampedusa is a key destination for such boats and many residents have long complained that the authorities in Italy and the European Union are not doing enough to deal with the thousands of migrants who come ashore each year.
Jose Manuel Barroso and Enrico Letta visited the temporary mortuary holding the coffins of the victims and met survivors and those who had helped in the rescue.
The two men were heckled on their arrival in Lampedusa, with shouts of “disgrace” and “killers”.
Speaking at a joint news conference, Jose Manuel Barroso said he would never forget the sight of hundreds of coffins.
“It’s something, I think, one cannot forget: coffins of babies, coffins of a mother and a child that was born at that moment,” he said.
“This is something that profoundly shocked me.”
Jose Manuel Barroso said he also met survivors who had retained hope, and it was now the duty of the EU “to give reason for that hope”.
He said 30 million euros would help Italy to settle its refugees, and listed a range of measures the EU must undertake including focusing their efforts on the people smugglers and the countries where most of the migrants are coming from.
Jose Manuel Barroso also said the EU parliament would be voting on a plan to launch Mediterranean-wide search and rescue patrols to intercept migrant boats.
The European Commissioner for Home Affairs, Cecilia Malmstroem, said on Tuesday she had asked the EU’s Frontex border agency to draw up a “concrete proposal” for an operation that would allow better tracking, identification and rescue of migrant boats.
Frontex currently helps Italy to intercept migrant boats, but the two EU operations in the southern Mediterranean have limited resources – a total of four ships, two helicopters and two planes.
PM Enrico Letta said a great human drama was unfolding on Lampedusa and pledged to put the issue of migration at the centre of the EU agenda.
The two were met upon their arrival in Lampedusa by a small group of activists and local residents who shouted “shame”, “disgrace” and “killers” at the airport gates.
“They should be ashamed of themselves. They should solve this humanitarian problem,” one protester was quoted by Agence France-Presse news agency as saying.
The 66ft boat that sank last Thursday with more than 500 migrants on board had set off from Libya and was close to Lampedusa when, according to survivors, the engine failed.
In order to attract attention from passing boats, a small fire was lit which caused the passengers to panic and move towards one side of the boat which led to the capsizing, the survivors said.
Divers said they found dozens of bodies entwined together in the hull of the boat which lies about 155ft below the surface of the sea.
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