The European election campaign must not "paralyse" EU efforts to reform asylum rules which have split the bloc since the 2015 migration surge, commissioner Dimitris Avramopoulos says.
Merkel's two-day visit came four months after Greece emerged from its third and final bailout package.
Germany's interior minister is pressing ahead with controversial plans to hold asylum seekers in centres until their right to stay is determined.
The EU proposes financial incentives to member countries to admit migrants from Mediterranean rescue boats as part of efforts to defuse a weeks-long showdown with Italy.
German Chancellor Angela Merkel comes under fire from EU partners after she agrees to push back migrants in a last-ditch deal to save her fragile government.
EU leaders clinch a migration deal during all-night talks that Italy's hardline new PM said meant his country was "no longer alone" in shouldering the responsibility for migrants.
A row over how the European Union should deal with migrants crossing the Mediterranean has heated up in recent weeks, even though their number has declined sharply since 2015.