EU leaders have failed to reach agreement over who should get the top jobs to steer the 28-nation bloc over the next five years.
The outcome was "unfortunate but not dramatic", said European Council President Herman Van Rompuy, who stands down later this year.
"My conclusion was that we were not yet at the point where we could get a consensual solution on a whole package," Van Rompuy said after the talks dragged on into the early hours of Thursday.
There will be another summit on August 30, he said, adding he was "certain that ... we will reach a decision" then.
Early hopes for a decision on who would replace Britain's Catherine Ashton as foreign affairs head, a coveted high-profile job, faded from the start, putting the summit in immediate difficulty.
Without agreement on this key position, finding a new president of the European Council, which represents the 28 national leaders and sets overall policy direction, became even more difficult.
Rejecting suggestions of a setback, Van Rompuy said such decisions took time.
"I knew quite well that we might not reach a decision," he said, arguing that once Ashton's replacement is named, "this will all fall into place quite quickly".
German Chancellor Angela Merkel had played down expectations any decisions on appointments would be made even before leaders sat down at the summit table.
At the close of the meeting, Merkel said she was "fully confident we will get there, step by step, stage by stage.
"It is better to not have a deal because it's not yet possible to agree on a whole package of nominations," said Lithuanian President Dalia Grybauskaite as she left the meeting.
Grybauskaite had made clear from the start that Lithuania, along with the other Baltic states and Poland, would not accept the early favourite, Italian Foreign Minister Frederica Mogherini, as Ashton's replacement.
For them, Mogherini was too inexperienced while Rome has been too soft on Russia over the Ukraine crisis and too anxious to protect its important economic ties with Moscow.
Diplomats had said an alternative to Mogherini could be current EU Humanitarian Aid Commissioner Kristalina Georgieva of Bulgaria, who is close to the centre-right European People's Party, the biggest single group in the European Parliament.
As Mogherini's chances faded, Italian Prime Minister Matteo Renzi tweeted: "What does Italy ask for? Not one post or another, it asks for respect."
For the European Council, Danish Prime Minister Helle Thorning-Schmidt, a Social Democrat, enjoyed wide support, including from Britain, to replace Belgium's discreet but effective Van Rompuy.
Denmark, however, is not a member of the eurozone, a drawback especially for France.
French President Francois Hollande, however, stressed that what counted was "less the person than the policy ... and it is such considerations which will determine my decision".
Other names mentioned included conservatives Irish Prime Minister Enda Kenny and former Latvian premier Valdis Dombrovskis. Estonia's Andrus Ansip, who stepped down earlier this year, or Dutch Premier Mark Rutte would suit the centrist Liberals.
Kenny, however, dismissed the idea he could take the post, saying: "I have enough on my plate already!"
Once the top jobs are settled, then the EU embarks on the next round, deciding who gets which portfolio in the new 28-seat European Commission to be headed by Jean-Claude Juncker.
On Tuesday, the European Parliament confirmed veteran EU insider Juncker as head of the bloc's executive arm.
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