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Chancellor Angela Merkel has said the "breathtaking" flow of migrants into Germany will "occupy and change" the country in the coming years.
She said Germany would speed up asylum procedures and build extra housing, having pledged to spend €6bn (£4.4bn).
But she added that Germany could not solve the crisis on its own and urged all EU states to take in refugees.
About 20,000 migrants are thought to have entered Germany over the weekend and 11,000 are expected on Monday.
The flow of migrants across Europe shows no sign of easing, with crowds reported to be streaming across Hungary's border with Serbia.
Earlier, French President Francois Hollande announced that France is ready to take in 24,000 refugees to help deal with the crisis.
Mr Hollande said he and Mrs Merkel wanted the EU to back a plan under which each country would be obliged to take its fair share of migrants.
New quotas drawn up by the European Commission are set to be unveiled on Wednesday.
Spanish newspaper El Pais reported on Monday (in Spanish) that 120,000 migrants will be resettled under the proposals, on top of the 40,000 already agreed.
The 160,000 are said to include 66,000 who have arrived in Greece, 54,000 in Hungary and 40,000 in Italy.
In other developments:
Thousands of migrants who had arrived in Hungary made their way through Austria to Germany over the weekend. Those arriving at Munich station were cheered by locals.
Mrs Merkel thanked volunteers who had helped and welcomed those arriving, saying they had "painted a picture of Germany which can make us proud of our country".
However, she said that although Germany was "a country willing to take people in", it was "time for the European Union to pull its weight".
Germany - which expects 800,000 asylum requests this year - could face costs of €10bn (£7.3bn) next year because of the influx, she added.