The high number of migrants arriving has rekindled a fierce debate in Europe on how to share responsibility for the tens of thousands reaching the continent each year.
"Irregular migration is a European challenge and it needs a European answer," European Commission President Ursula von der Leyen said during a visit to Lampedusa, offering a 10-point plan to help Rome deal with the crisis.
Since Monday, about 8,500 people – more than the island's entire local population – have arrived in about 200 boats, according to the UN migration agency.
Lampedusa, Italy's southern-most island, has long been a landing point for migrant boats from North Africa.
But this week officials said its migration centre, built to house fewer than 400 people, was overwhelmed.
"We are doing everything possible," Italy's Prime Minister Giorgia Meloni said alongside Ms von der Leyen on Lampedusa.
It is "the future that Europe wants for itself that is at stake here, because the future of Europe depends on Europe's capacity to face major challenges".
Ms Meloni has called on Italy's EU partners to take more of the migrant burden.
The Italian Red Cross, which runs the overcrowded Lampedusa migration centre, said on Sunday that 1,500 migrants remained there despite it having a capacity for only 400.
Transfers of migrants to Sicily and the mainland have not kept up with the flow of new arrivals, although more transfers were expected to be made Sunday, the Red Cross said.
Italy migrant boat tragedy - in pictures
Unhappy Lampedusa residents were there to meet Ms Meloni and Ms von der Leyen at the island's airport, at one point threatening to block their motorcade.
"We've had enough of the island being used as a platform" by politicians, one fisherman told Ms Meloni.
"We're doing everything we can," she replied. "As usual, I'll take personal responsibility".
Ms von der Leyen said her aid plan for Italy included increased support for the European Agency for Asylum (EUAA) and the EU's Frontex border control agency to register new arrivals.
The increased measures include ensuring that fingerprints are taken and interviews are conducted to make sure people are directed towards the proper authorities.
The EU will also increase aid for moving asylum seekers from Italy to other EU members, under a voluntary scheme for sharing responsibility for migrants, particularly women and unaccompanied minors.
The plan is designed to combine a firm stance against smugglers, with legal channels of entry into the EU for those eligible for asylum.
But the EU plan for sharing the burden of new arrivals has met resistance in several bloc members, with right-wing governments in Poland and Hungary the most strongly opposed.
This week, Germany said it had stopped accepting migrants living in Italy under the European solidarity scheme, saying Rome was failing to honour its obligations under EU rules.
Under the bloc's so-called Dublin procedure, irregular migrants must be registered in the EU country they first enter. If they later travel to another nation in the bloc, they can be returned to their first EU port of call.
"That is why we have sent a signal to Italy," a German government spokesman said Friday.
But Mediterranean countries such as Italy say the rules place an excessive burden on border nations, particularly since new arrivals often want to move on and live in other EU countries.
More than 127,000 migrants have arrived on Italy's shores so far this year, almost double the number in the period last year.
Ships operated by NGOs including Doctors without Borders (MSF) have rescued nearly 500 migrants in 11 operations in the Mediterranean in recent days, who were are headed for major Italian ports.
But dozens of small boats also continue to make the perilous sea-crossing to Lampedusa, which is only 145km off the coast of Tunisia.
In July, Ms von der Leyen, with Ms Meloni's strong backing, struck an agreement with Tunisia aimed at curbing the flow of irregular migration from the North African country.
More than 2,000 people have died this year crossing from North Africa to Italy and Malta, according to the UN migration agency.