About 13,00 refugees were expected to reach Munich's main railway station on Saturday, as local officials warned of a lack of accommodation for the new arrivals in the Bavarian capital.
The Bavarian government said that some 9,000 people had disembarked in Munich by early evening, most after having made long and dangerous journeys out of war-torn countries such as Syria and Iraq.
Foreign Minister Frank-Walter Steinmeier said Friday that 40,000 could arrive in the country over the weekend.
But Germany's integration commissioner, Aydan Ozoguz, said that although the pace was "breathtaking," she was unsure if the foreign minister's estimate would bear out.
Christoph Hillenbrand, head of the eastern Bavarian regional authority, called for urgent assistance from other parts of Germany, saying Munich was short 3,000 to 5,000 beds.
Authorities there were considering whether to open the multi-purpose Olympiahalle arena for short-term accommodation. Tents were also to be erected on Sunday in the city, which already welcomed 40,000 migrants in the week prior.
The Interior Ministery said it was trying to relieve the pressure on Munich, often the first stop for refugees traveling by rail to Germany before they are resettled elsewhere in the country.
A large refugee center would be built in the northern town of Lueneburg, the ministry said, and some trains were bypassing Munich altogether, such as one to the western city of Dusseldorf on Saturday carrying 900 people.
In Berlin, where 5,500 refugees arrived over the course of the past week, troops helped set up accommodation at the city's Olympic Park.
According to official figures, 37,000 refugees were registered in Germany September 1-8. About 450,000 have arrived so far this year, a figure expected to rise to 800,000 by the end of the year.
In her weekly podcast, German Chancellor Angela Merkel called on the refugees to learn German.
"And then make contact and don't retreat into yourselves by living and working in the community you know. Try to get out," Merkel said, voicing concerns of many that the new arrivals will not integrate readily.
Merkel also appealed to women to become involved in social initiatives which would welcome any woman "who, so to speak, puts her feelers out."
Germany's mass circulation Bild tabloid on Saturday carried an interview with Hungarian Prime Minister Viktor Orban, in which he called for the refugees to "go back to where they came from."
Noting that many of the Syrian refugees had started out on their journeys to Europe, not from war-torn Syria, but from camps in neighboring countries, Orban said: "They were safe there. These people are not fleeing danger."
The outspoken nationalist leader said he had nothing in principle against people seeking economic betterment, "but one thing is clear: There is no basic right to a better life, only a right to safety and dignity."
German Deputy Chancellor Sigmar Gabriel was sharply critical of Orban, saying Hungary's leader was bound by European law on refugees.
Speaking at a party conference of Germany's Social Democrats in the northern city of Hildesheim, the SPD leader said Orban could not leave the refugees in poor conditions and then deport them.
In remarks to German newsmagazine Der Spiegel, Austrian Chancellor Werner Faymann compared Orban's actions with the racial policies of the Nazis.
"Subdividing human rights by religion is unacceptable," the Social Democrat leader said.
"Sticking refugees on trains in the belief that they will go somewhere else completely, calls up memories of our continent's darkest era," Faymann said.
He raised the possibility that Hungary, a net recipient of EU structural funding, could be denied such funding unless it agreed to take in refugees.
Orban's government has rejected moves to set up a quota system for EU member states to accept refugees.
However, Orban received backing on Thursday for his strong stance against Germany's open-door refugee policy from Horst Seehofer, prime minister of Bavaria and, as leader of the Christian Social Union (CSU), a key ally in Merkel's coalition government.
Seehofer termed the chancellor's decision last weekend to allow refugees in Hungary to proceed unhindered to Germany "a mistake that will long hang over us" and issued an invitation to Orban to join him in seeking a solution to the burgeoning crisis.
The Austrian press agency reported Saturday that around 6,000 refugees had arrived in Nickelsdorf, a small Austrian town on the border with Hungary that has become a transit point for migrants trying to get to Germany.
By Sabine Dobel
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