EU heads of state and government, who were gathered in Brussels to select, among other roles, someone to replace Jean-Claude Juncker as the EU Commission President, will meet again on Tuesday, said a spokesperson for EU Council chief Donald Tusk.
The gathered leaders would in the meantime focus on bilateral meetings, Efe news reported, citing diplomatic sources in Brussels as saying.
They travelled to Brussels on Sunday for the crunch summit which aimed to appoint new faces to not only the Commission but also the Council, the European Central Bank and Foreign Policy.
While a host of senior roles were up for grabs, media attention was focused largely on the post of Commission President.
EU nations like Spain, France, Germany and Tusk have proposed Dutch politician Frans Timmermans, a member of the Party of European Socialists (PES) and currently a Vice-President at the Commission, for the post of Commission President.
Sources from the delegation travelling with Spain's Prime Minister Pedro Sánchez have confirmed the country's support for the Dutchman.
European leaders tied to the bloc's centre-right People's Party (EPP) and several Eastern European nations have resisted the proposal.
The EPP has presented its leader, German politician Manfred Weber, for the job.
The top roles must be shared out in a way that satisfies the main parties in the European Parliament, the PES, the EPP and the Liberals (ALDE), following elections in May.
ALDE has put forward Dane Margrethe Vestager for Commission chief.
Not only must the mainstream parliamentary groups strike a consensus but the sharing out of the posts must respect a geographical balance.
Although the fate of the EU's institutions is currently in the hands of the EU's 28 leaders, the issue could also be put to a vote in the Council, where a candidate needs the support of at least 21 countries that represent at least 65 per cent of the EU's population.
It could also go before lawmakers at the European Parliament, where a candidate needs an absolute majority.
Italy's Prime Minister Guiseppe Conte spoke against the possibility of Timmermans becoming Commission chief and suggested that the future leader did not necessarily have to be one of the leading Spitzenkandidaten, as the candidates are known.
The stuttering decision making at the EU forced Finland to postpone its official presentation taking over the rotating presidency of the EU Council.
"Morning has broken at 6.30 after a sleepless night in Brussels. And the #EUCO just continues and continues..." its official Twitter page said.
The outgoing officials are Juncker, Tusk, European Central Bank's President Mario Draghi and High Representative of the Union for Foreign Affairs and Security Policy Federica Mogherini.
( With inputs from IANS )