German Chancellor Angela Merkel has pressed fellow European nations to share the burden of the influx of migrants.
The German leader told reporters in Berlin that the European Union will betray its values if it fails to get a grip on the crisis.
Germany has taken more asylum seekers than any other EU country and is one of only a handful of nations that has accepted significant numbers. It expects about 800,000 migrants to arrive this year; about four times the number it saw in 2014.
Mrs Merkel renewed calls for quotas to spread the migrants out among more countries in the 28-nation EU, a call that has run into stiff resistance - in particular from eastern nations including Slovakia, the Czech Republic, Hungary and Poland.
"Europe as a whole must move and its states must share the responsibility for refugees seeking asylum," she said.
"Universal civil rights so far have been closely linked with Europe and its history - it was one of the founding motives of the European Union," she said. "If Europe fails on the question of refugees, this close connection with universal civil rights ... will be destroyed and it won't be the Europe we want."
Mrs Merkel said of talks with other EU nations that "there's no point in publicly calling each other names, but we must simply say that the current situation is not satisfactory".
She was openly critical of the idea of giving priority to refugees who are Christians - a preference voiced by Slovakia. She said Europe's values are based on the dignity of every individual, and that saying Muslims are not wanted "can't be right".
In Germany itself, refugees have largely been welcomed though increasing attacks on migrants and shelters have alarmed authorities.
Mrs Merkel promised to use "the full force of the law" against those who abuse or attack migrants or their accommodation.
"There is no tolerance toward those who question the dignity of other people," she said, urging Germans to "keep your distance" from anti-migrant protests.