BRUSSELS – A summit of the European Union’s 27 national leaders, charged with agreeing on a long-term budget for the bloc, broke up Friday afternoon without being able to reach a deal.

Coming just days after the 17 eurogroup finance ministers failed, yet again, to agree on the conditions for releasing badly needed bailout money for Greece, the failure of the two-day summit raises questions about how the bloc makes important decisions. In most cases, unanimity is required, meaning that each country wields veto power.

The EU’s top officials, who put in long hours trying to soften up the national leaders individually before putting them together in the same meeting room, tried to put a brave face on the budget deadlock.