Italy's Prime Minister warned Sunday that the "future of Europe is at stake" after droves of migrants landed on the Mediterranean island of Lampedusa. 

Thousands of migrants on vessels from the North African coast landed on Italy's southernmost island this week, sparking a crisis that has rekindled debate over the division of responsibility among the EU nations.

At a press conference with European Commission President Ursula von der Leyen during a visit to the island, Giorgia Meloni said the bloc needed to work together to face the challenges of uncontrolled migration. 

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," Meloni said.

Between Monday and Wednesday, around 8,500 people, more than the island's entire local population, arrived in 199 boats, according to the UN migration agency.

"Irregular immigration is a European challenge that needs a European response," von der Leyen said, calling on other members of the bloc to take in some of the migrants.  

The Italian Red Cross, which runs the overcrowded Lampedusa migration-center, said Sunday that 1,500 migrants remained there despite having a capacity for just 400. 

Transfers of migrants to Sicily and the mainland have not kept up with the flow of new arrivals, although further transfers were expected to be made Sunday, the Red Cross said. 

The officials were met on arrival at the airport by residents unhappy with the mass arrivals, threatening to block their motorcade.

"We are doing everything possible," Meloni had said in response.

Large vessels operated by NGOs like the Geo Barents by Doctors Without Borders (MSF), which have rescued nearly 500 migrants in 11 operations, are headed for major Italian ports. 

But dozens of small boats continue to make the perilous sea-crossing to Lampedusa, where the migrant management system has come to the brink of asphyxiation. 

In July, von der Leyen, with Meloni's strong backing, struck an agreement with Tunisia aimed at curbing the flow of irregular migration from the North African country.

More than 127,000 migrants have arrived on Italy's shores so far this year, almost double the same period last year.

Over 2,000 people have died this year crossing from North Africa to Italy and Malta, according to the UN migration agency.

The EU is pushing to overhaul rules on how to handle the migrant flow.

In France, members of the far right say Paris should not allow any migrants from Lampedusa across the border from Italy.

However, French government sources said late Saturday that Meloni and French President Emmanuel Macron had spoken and agreed on the need to "strengthen cooperation at the European level."