The German leader told reporters in Berlin the EU 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.
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, Czech Republic, Hungary, and Poland.
“Europe as a whole must move and its states must share the responsibility for refugees seeking asylum,” she said.
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”.
Meanwhile, France plans to build a camp this winter for as many as 1,500 migrants in the northern port city of Calais where twice that many are living in tents and hoping to make the sea-crossing to Britain.
European Commission vice president Frans Timmermans, visiting Calais with French prime minister Manuel Valls, said the commission would contribute €5m to the new centre which will house people in tents.
Calais mayor Natacha Bouchart said the facility would be welcome but fell short of what was needed.
“It’s a gesture but a pretty feeble gesture, it’s €25m that would be needed,” she said.
Interior ministers are meeting in September and EU leaders on November 11 to try to agree on a response to a crisis.
Meanwhile, Austria has stepped up inspections at its Hungarian border after 71 migrants were found suffocated in a truck.
The increased security measures created a 30km traffic jam on the Budapest-Vienna highway.
And in Germany, the state government in Bavaria, which has all of Germany’s border crossings with Austria, said that it had launched special traffic checks on roads leading to the border.