Germany can cope with at least 500,000 asylum-seekers a year for several years, Vice Chancellor Sigmar Gabriel has said.
Officials have said they expect more than 800,000 asylum-seekers in 2015 alone – four times the 2014 figure.
Mr Gabriel repeated that other European countries should take their fair share.
The UN’s refugee agency, UNHCR, says a record 7,000 Syrian refugees arrived in Macedonia alone on Monday and 30,000 migrants were on Greek islands.
The migrant influx has unsettled European governments and prompted diverse responses – Hungary’s conservative leadership has been building a border fence to try to keep them out while the German leadership expresses pride in crowds who turned out to welcome them in.
A Greek minister said on Monday that the island of Lesbos, which sits off the Turkish coast, was “on the verge of an explosion” due to a build-up of 20,000 migrants trying to reach the European mainland.
The government and UNHCR have brought in extra staff and ships to process the migrants.