EU leaders meeting in Brussels remain divided over who should get the EU’s top jobs, and talks have been suspended until Tuesday.
They are arguing mainly over a successor to Commission President Jean-Claude Juncker. They had hoped to get a deal on Sunday night.
Diplomats say summit chair Donald Tusk proposed Dutch centre-left politician Frans Timmermans to succeed Mr Juncker.
Centre-right Bulgarian Kristalina Georgieva would replace Mr Tusk.
Late on Sunday the summit was suspended so that Mr Tusk could hold bilateral talks, seeking a breakthrough. Talks then resumed over breakfast on Monday but were later suspended until 11:00 (09:00 GMT) Tuesday.
Both German Chancellor Angela Merkel and French President Emmanuel Macron said choosing the candidates was now more complicated because the May European elections had ended the traditional centre-left and centre-right dominance of EU politics.
“When you have not just two partners, but three or four, the issue is not clearly defined,” Mrs Merkel told reporters, admitting that the disagreement “looks bad”. “But a compromise must be found – historically it’s immaterial if this takes a bit longer.”
The May elections saw big gains for the liberals – including Mr Macron’s alliance – and Greens, as well as for nationalists. But no group has a majority.
President Macron told reporters: “we must learn from this setback – we’re projecting an image of Europe which isn’t serious, and we need better preparation for these meetings”. He lamented that “what’s lacking is a feeling and duty to defend Europe as a whole”.
What compromise was put forward?
The rare Sunday summit was called because EU leaders failed on 20 June to agree on candidates for the Commission president’s job and other top posts: European Council president (to replace Donald Tusk); High Representative for foreign policy (to replace Federica Mogherini); European Parliament president and European Central Bank president.