European leaders failed to agree on a new top team to lead efforts to reform their union for the next five years, and postponed a decision for a least a week.

The 28 heads of government met for dinner after Brussels' main political factions refused to fall into line behind a single choice to head the European Commission.

The successor to Jean-Claude Juncker at the head of the EU executive is the key leadership role in Brussels, and without a nominee the leaders were also not able to agree the broader package of appointments, forcing them to call a crisis summit for Sunday, 30 June.

"The European Council has had a full discussion of nominations," summit host Donald Tusk, the president of the leaders' council, said. "There was no majority on any candidate.

"The European Council agreed that there has to be a package reflecting the diversity of the EU. We will meet again on June 30." 

The new summit comes just two days before the new European Parliament begins its first session, and the leaders are determined to agree on key appointments before lawmakers choose their own parliamentary president. 

French President Emmanuel Macron said parliament's "lead candidate" process for choosing a commission president is unworkable and that the 28 national leaders must decide.

But Germany's Chancellor Angela Merkel defended the political process, and noted that whichever name the leaders come up with will still have to be approved by a majority of MEPs in the assembly.

"Here it has emerged ... that there is no majority for one of the top candidates of the political parties," she said.

"We naturally want a joint solution with the parliament."

Hard man to replace

None of the leading names to have emerged during last month's election have won consensus among four main parliamentary parties to replace Mr Juncker as president of the EU's executive arm.

"I note with satisfaction, amusement and, yes, pleasure that it seems it is not easy to replace me," Mr Juncker joked.

Other jobs up for grabs include President of the European Parliament, which will sit for the first time on 2 July, a replacement for Mr Tusk as President of the European Council, and foreign policy chief.

National leaders want to control the process and dole out the most senior jobs in a way that balances men and women, east and west Europe, small countries and large.

But the results of May's European elections forced the main conservative, socialist, liberal and Green parliamentary blocs to form a majority coalition.

The parties, while working to draft a joint political programme, have not united behind a particular package of candidates.

German conservative MEP Manfred Weber, whose centre-right EPP group took the biggest single bloc of seats, failed to win over Dutch social democrat Frans Timmermans' S&D or the liberal Renew Europe group, which has backed Danish commissioner Margrethe Vestager to take over from Mr Juncker.

Prize posts

Whoever is eventually the nominee for the commission presidency must win the backing of least 21 of the 28 EU leaders and a majority in the 751-member parliament.

According to three sources close to the negotiations, the leaders had been expected to agree that the EPP will be allowed to propose an alternative to Mr Weber.

Renew Europe hopes to see a liberal replace Mr Tusk as president of the European Council, and the socialists will provide a foreign policy chief.

Finally, the Greens could share the job of presiding over the five-year parliament with the socialists, with each providing a speaker for two-and-a-half years.

One option for commission president might be Europe's ambitious Brexit negotiator, Michel Barnier, a former French minister who is also a member of Ms Merkel's EPP.

But the party is said to have other names up its sleeve and French and German sources agree that the chancellor is not ready to cede the prize to a Frenchman.

Fine Gael, being members of the EPP, support the candidacy of Mr Weber.

Speaking on RTÉ's Morning Ireland, Minister of State for European Affairs Helen McEntee said their position has not changed.

"Manfred Weber, being the EPP candidate, is still our candidate, and that's still our position," Ms McEntee said.

"Michel Barnier is someone we've worked very closely with and we respect, but  he is not a candidate as of yet. Unless we get to that position, we're focusing on the candidates we have."

Ms McEntee said that if things change and candidates are added, then the Irish Government is open to discussion.

The six EU leaders invited to the G20 summit in Osaka on Friday and Saturday next week - from France, Germany, Britain, Italy, Spain and the Netherlands - will continue the discussion there before returning to Brussels on 30 July.