"I am very worried. Today it is on this issue that Europe will either rediscover its soul or lose it for good," he warned.
He then urged Italy's EU partners to stop squabbling and start working on a common solution to the crisis.
The alternative, he warned, would be the inevitable collapse of the Schengen accords which allow free travel across much of continental Europe.
In Germany, meanwhile, Vice Chancellor Sigmar Gabriel and Foreign Minister Frank-Walter Steinmeier, a fellow Social Democrat, issued a joint call for the EU's asylum policy to be revamped.
"It is necessary to share out refugees in Europe fairly," the two said in the Sunday edition of the Frankfurter Allgemeine newspaper.
They also called for a "European asylum code" that would guarantee EU-wide asylum status.
EU interior and foreign ministers will discuss the migrant crisis in mid-October, ahead of a summit in Malta in November, French Interior Minister Bernard Cazeneuve said Thursday.
