Germany can cope with at least 500,000 asylum seekers a year for several years, Vice Chancellor Sigmar Gabriel has said.
Germany expects more than 800,000 asylum-seekers in 2015 alone – four times the 2014 figure.
Mr Gabriel reiterated that other EU states should share the burden.
The UN’s refugee agency, UNHCR, says a record 7,000 Syrian migrants arrived in Macedonia alone on Monday and 30,000 were on Greek islands.
The migrants, mainly Syrians, are engaged in a long trek which takes them from Turkey, across the sea to Greece, through Macedonia and Serbia, and then to Hungary from where they aim to reach Austria and Germany.
The migrant influx has unsettled European governments and prompted diverse responses. Hungary's conservative leadership is building a border fence to try to keep them out, but German politicians have expressed pride in crowds who welcomed new arrivals. 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. The government and UNHCR have brought in extra staff and ships to process them. Source: BBC