BRUSSELS — Days after a wave of deportations of migrants arriving in Europe from Turkey, the European Union’s executive arm proposed a new quota system for members accepting asylum seekers to ease the burden on the nations confronted with an overwhelming influx.

The quotas were part of a plan introduced Wednesday by the European Commission, the bloc’s executive arm, to address the continent’s ineffective asylum system while avoiding a backlash from member states reluctant to accept a larger number of migrants.

The proposals would create a quota mechanism to deal with exceptional situations when a country is confronted with an unmanageable crisis. An alternative would allow for the establishment of a permanent system to redistribute asylum seekers.

The second option would amount to a permanent program to shift asylum seekers around Europe, and it is likely to antagonize countries like Hungary and Slovakia, which bluntly oppose any measures to force them to take in migrants and which argue that quotas encourage migration to the Continent.