In an interview with the Passauer Neue Presse, the German Social Democratic Party (SPD) politician said there should be more legal ways into Europe for migrants and a new quota system for sharing refugees among European countries.
EU foreign and interior ministers agreed to double the resources allocated to the Union's Triton Mediterranean border control programme at a meeting in Luxembourg on Monday.
The new funds will let countries deploy more ships to help beleaguered Italian navy and coastguard vessels.
EU heads of state and government will also meet on Thursday at a special summit to discuss the Mediterranean.
Share the load
German Development Minister Gerd Müller told Bild on Tuesday that Europe needed an “immediate restart of 'Mare Nostrum' [a former Italian sea rescue programme ended in late 2014] and a whole concept for taking on and distributing refugees, involving all 28 EU nations”.
Schulz agreed that Europe needed a new quota system.
“Those EU member governments that weren't doing enough until now have to start moving,” he said.
Germany, France and Sweden have so far played host to the lion's share of refugees arriving in the EU.
Interior Minister Thomas de Maizière confirmed that the German government would push others to share the burden.
He added that he had pushed officials in Greece and Italy – the countries where many refugees first cross into the EU – to improve their registrations of new arrivals.
“From that point on there ought to be a fair distribution among all European countries,” he told ARD television.
Meanwhile, EU Budget Commissioner Kristalina Georgieva told business daily Handelsblatt that more help for refugees was “not primarily a question of the European budget, but of political will. It's up to the member states.”
But differences were already beginning to appear between Germany's two biggest parties on how best to deal with the crisis.
SPD leader in the Bundestag (German parliament) Thomas Oppermann told Bild that “we must point out legal ways to cross the Mediterranean to African refugees”.
But Christian Democratic Union (CDU) politician and leader of the conservative European People's Party (EPP) in the European Parliament Manfred Weber said that north African countries should be “supported to improve their border security”.
He told the Mittelbayerische Zeitung on Tuesday that “we can't solve Africa's problems with mass migration into Europe”.