The haggling over jobs, including a replacement for EU Commission President Jean-Claude Juncker, is likely to last several months.
For the first time the big centrist blocs no longer have a majority as the European Parliament elections boosted
nationalists, the Greens and liberals. It leaves the EU more fragmented, so finding consensus may be harder than in the past, the BBC reported.
The talks over dinner on Tuesday may not even result in a shortlist of candidates. Outgoing UK Prime Minister Theresa May will participate, but reports say that there will be little or no discussion of Brexit.
It is more an occasion for leaders to assess the political mood and explore possible combinations, to ensure a stable balance of political opinions, geography and gender.
The other top EU officials to be replaced later this year are: European Council President Donald Tusk (Polish), European Central Bank President Mario Draghi (Italian) and EU High Representative for Foreign Affairs Federica Mogherini (Italian).
The new top officials will take up their posts on November 1, except for the new European Council chief, who starts on December 1.
In 2014, Juncker was chosen to head the Commission as the centre-right European People's Party candidate, after the EPP had won the election.
But it is a much tougher challenge this time for the EPP's candidate Manfred Weber - a German - after his bloc shrank from 217 seats to 180 in the 751-seat Parliament. He has the backing of German Chancellor Angela Merkel.
On the selection of the European Commission President, the European Parliament said the winner only had to be someone "who made his/her programme and personality known prior to the elections and engaged in a European-wide campaign".
That opens the door to candidates who weren't strictly candidates before, such as Denmark's Margarete Vestager or maybe even the Chief Brexit negotiator Michel Barnier, the BBC said.
( With inputs from IANS )