The EU's Economic Affairs Commissioner Pierre Moscovici said he believed "more than ever" that a debt deal was possible between Greece and its creditors.
Greek Finance Minister Yanis Varoufakis warned that EU leaders had a duty to avoid a historic "failure" and urged a swift accord in Greece's debt talks with its creditors.
Prime Minister David Cameron was put on notice that 50 of his own backbenchers will lead calls for Britain to quit the EU if he does not secure major concessions from Brussels.
European Commission head Jean-Claude Juncker said that "challenging" negotiations with Greece would continue, after late-night talks with premier Alexis Tsipras broke up without a deal.
European parliament head Martin Schulz said the Russian ambassador to the EU was barred access to the institution in retribution for a travel ban imposed by Moscow.
Britain could lose its prized EU veto on some subjects if it opts out from the commitment to "ever closer union" in the bloc's treaties under David Cameron's reform plans.
Macedonian political leaders agreed to hold elections in early 2016 in order to overcome a deep political crisis, EU enlargement commissioner Johannes Hahn said.
Russian Foreign Minister Sergei Lavrov dismissed the "absurdity" of EU complaints over a travel ban imposed by Moscow on 89 Europeans over the Ukraine crisis.
Germany and France urged the EU to find a fairer way to admit and distribute asylum seekers, as their leaders met the European Commission chief in Berlin.
French Foreign Minister Laurent Fabius said a British referendum on whether to leave the EU was "very risky", ahead of a visit by Prime Minister David Cameron to Paris.
EU foreign policy chief Federica Mogherini called on Israel and the Palestinians to resume peace negotiations, saying the situation on the ground was "not sustainable."