The EU congratulated Alexis Tsipras on his left-wing party's re-election victory and said Greece has "no time to lose" in implementing the reforms agreed as part of its international bailout.
German Foreign Minister Frank-Walter Steinmeier said that EU members reluctant to accept migrant quotas may have to be outvoted and overruled in the 28-member bloc.
The European Union has announced an emergency summit in Brussels next in a bid to find solutions to the continent's worst refugee crisis since World War II.
EU president Donald Tusk said he would consider requests by German Chancellor Angela Merkel and others for an emergency summit on migrants and decide later this week.
German Chancellor Angela Merkel urged the EU to agree to a proportional distribution of refugees with no limits on actual numbers, going much further than plans unveiled by the European Commission.
Germany's Interior Minister Thomas de Maiziere said Europe should stop looking on helplessly as "murder" rages on in Syria, as he called on the bloc to review its strategy on the conflict.
EU president Donald Tusk urged a crackdown on the "murderers" among human traffickers who have killed scores of people trying to reach Europe from conflicts abroad.
British Prime Minister David Cameron suffered an embarrassing defeat in parliament over how the referendum he has called on leaving the European Union will be conducted.
Turkish Prime Minister Ahmed Davutoglu criticised the "ridiculously small" share of refugees the EU is accepting, labelling the continent the "Christian fortress Europe."
The EU is preparing to step up action against people smugglers in the Mediterranean, actively seizing the boats which carry thousands of hapless migrants to Europe.
A market in fake Syrian passports has sprung up, particularly in Turkey, to help migrants and refugees enter the EU, the head of Europe's border agency Frontex said.
EU foreign policy chief Federica Mogherini expressed concern over "very worrying" deadly clashes in Kiev as Ukrainian lawmakers backed an autonomy plan for rebel regions.