EU leaders met without Theresa May on Thursday and launched the process of divvying up the bloc’s top jobs, with the European council president, Donald Tusk, announcing a strategy that could see the UK outvoted. Before the end of the year five EU jobs will fall vacant, including the presidents of the European commission, European central bank and Tusk’s own position.

At the meeting in the Romanian city of Sibiu, called to look ahead to the EU’s post-Brexit future, Tusk said he wanted EU leaders to agree nominations in June, saying decisions could be made via qualified majority voting if there was no unanimity. “Consensus is always better than voting,” he told journalists after the summit. “But I have no illusions that consensus will be easy or possible. And I will not wait three months.”

EU leaders, including the British prime minister, will get their say at a special summit on 28 May, soon after European elections. In theory May could find herself overruled, as David Cameron was in 2014 when he tried unsuccessfully to block the appointment of Jean-Claude Juncker.

Earlier in the day EU leaders pledged to stick together “through thick and thin”. Asked as he left the press conference whether Brexit had been discussed, Tusk said: “No, oof, no,” and headed for the door.

Falling on the EU’s self-declared “Europe Day”, the summit was conceived as a show of unity. It was the third time the leaders have gathered without the British prime minister since the Brexit referendum, following a gathering in Bratislava in 2016 and another in Rome in 2017 to celebrate the European project’s 60th birthday.

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Despite the pledges of unity, divvying up the top posts is already causing splits. The bloc is divided on the process of allocating jobs, with the European parliament favouring a system of lead candidates – spitzenkandidaten – linked to election results. That process could see the relatively inexperienced German MEP Manfred Weber become the next commission president. He would be the first commission leader in a generation not to have led a government.

But many EU leaders object to ceding control over the process to the parliament. Under EU law, European leaders nominate new leaders, who must be approved by MEPs.

The so-called Sibiu declaration, which resembles a one-page motivational letter, was replete with pledges of solidarity, fairness and a desire to “develop the rules-based international order”. It also revealed how the EU is seeking to move on from Brexit, with a declaration that it was “a new union at 27 ready to embrace its future as one”.

But leaders were unable to completely avoid questions on Brexit. Asked whether he wished May was at the summit, Juncker said: “I am missing her.”

The European parliament president, Antonio Tajani, sounded a more impatient note, saying he hoped “the British will decide as soon as possible” what they were going to do. “Months have gone by … And it is difficult to understand what is going on.”

French president Emmanuel Macron argued that young British people had failed to realise Brexit would affect them and now faced being shut out of Europe’s future.

“I very often think about the British young people,” Macron said. “At some point in time, they thought Brexit, the referendum was not about them. They did not go and vote, most of them, many of them, but they woke up right after the Brexit vote. And the Europe of the future will be about climate choices, geostrategic choices, choosing an economic model and all of that will bear fruit in ten or twenty years, so it is your Europe that is being decided on today.”

Outside the summit’s secure perimeter, the UK Brexit secretary, Stephen Barclay, said Britain’s departure from the EU was “an opportunity to be seized” as he gave a speech covering migration, security and climate change.

Speaking at a thinktank event, Barclay voiced frustration with “the narrative within Europe”, saying Brexit was “an opportunity of confidence and optimism, a desire to be more global. It certainly wasn’t the Nigel Farage little Englander portrayal of Brexit.”

“I think there is lazy thinking, to be frank, on Brexit and a failure to look at the longer-term relationship between the United Kingdom and Europe,” he said.

He was greeted with polite applause from the audience, but also scepticism. “Brexit, it’s a lose-lose agenda for the UK and for Europe,” said a fellow panellist, Luca Jahier, the president of the European economic and social committee.