Germany expects at least 800,000 asylum seekers this year - about four times the number it handled last year. It has urged its EU partners to back mandatory quotas - something that France, Italy and Greece also want.
Mrs Merkel's Bavarian allies, the CSU, called Berlin's approach to migration "an unparalleled political error". Other German regional leaders have also criticised the policy.
Germany said it would take in Syrian refugees wherever in the EU they had first arrived. Sweden had earlier announced a similar policy.
It means that the EU's Dublin Regulation is de facto suspended. That rule says a migrant's asylum claim should be processed in the European country where he/she first arrives.