Theresa May has arrived in Brussels for talks aimed at allocating the European Union’s top jobs, amid indications that the process has run into difficulties.

The Prime Minister said she would play a “constructive role” in the discussions, in what is expected to be her final European Council summit.

But moments earlier Donald Tusk said that while he had been “cautiously optimistic” about making progress, he was now “more cautious than optimistic”.

If the talks fail to make progress, Mrs May – or her successor – could be forced into attending another summit to settle the issue.

The European Council president’s pessimistic assessment followed a round of talks before the summit, including with German Chancellor Angela Merkel and French President Emmanuel Macron.

Mr Tusk said on Twitter: “Last round of consultations on appointments before the start of #EUCO (the European Council).

“Yesterday I was cautiously optimistic. Today I’m more cautious than optimistic.”

Arriving in Brussels, Mrs May told reporters: “We will be looking for the UK to do what we have always said we would do which is to make a constructive contribution as we remain a member of the European Union (and) for that period of time we will continue to meet our rights and obligations.

“But of course we will be leaving the EU and we look forward to developing a close partnership with the EU when we’ve left.”

She sidestepped a question over whether she would miss Council gatherings, but said: “I will continue to do what we have always done as a UK which is to play a constructive role within the European Union while we are part of the discussions around the table.”

It came after Irish Taoiseach Leo Varadkar said he did not think the EU leaders would be able to elect a new European Council or European Commission president on Thursday.

He told reporters as he arrived at the summit: “The sense I have is that we won’t be in a position to elect a new Commission president or a new Council president today, and the likelihood is that we will have to have another summit at the end of June or in early July.”

Leaders of EU countries will discuss who should take over from Mr Tusk and European Commission president Jean-Claude Juncker, but the UK is not expected to play a major role. 

A new European Council president, European Commission president, European Central Bank president and EU High Representative for Foreign Affairs and Security Policy will be decided in the talks.

It is not clear whether the “Spitzenkandidaten process” – in which political groupings in the European Parliament put forward their choices – will be used again, following its initiation in the 2014 elections.

But the main political groupings in the Parliament have nominated candidates, including German MEP Manfred Weber, for the centre-right European People’s Party (EPP), and former Dutch foreign minister Frans Timmermans, for the Party of European Socialists (PES).

French President Emmanuel Macron Mr Macron is thought to favour appointing the EU’s chief Brexit negotiator, Michel Barnier (Stefan Rousseau/PA)

The liberal group has put forward a “Spitzen Team” made up of figures including European Parliament Brexit co-ordinator Guy Verhofstadt and Danish EU Commissioner Margrethe Vestager.

However, Mr Macron is thought to favour appointing the EU’s chief Brexit negotiator, Michel Barnier, to the role, limiting Germany’s power in the bloc which would grow if Mr Weber became Commission president.

The successful candidate will take office on November 1.

The European Council president will be selected from a field of former heads of government and will assume the role on December 1.

EU leaders will also focus on climate, disinformation, the long-term EU budget and external relations at the summit, before discussing the bloc’s top jobs over dinner.