EUROPEAN leaders have challenged Theresa May over her refusal to guarantee the rights of EU citizens to remain in the UK after Brexit.

The European Council President Donald Tusk said the UK had to come up with a "serious response" on what will happen to EU citizens after the UK leaves.

"We need guarantees," Tusk said in Brussels as 27 EU leaders backed the bloc's Brexit negotiating guidelines.

The rights of EU citizens to live, work and study in the UK is one of three topics they want dealt with in the first phase of Brexit talks. Negotiations will start after the UK General Election on June 8.

Tusk made the remarks at a news conference after EU leaders – minus UK Prime Minister May – nodded through the guidelines in a matter of minutes.

"Over the past weeks, we have repeatedly heard from our British friends, also during my visit in London, that they are ready to agree on this issue quickly," he said. "But I would like to state very clearly that we need real guarantees for our people to live, work and study in the UK.

"The same goes for the Brits," living on the European continent, he continued.

UK citizens living in EU countries and non-UK EU citizens living in Britain are estimated at 4.5 million.

European Commission president Jean-Claude Juncker also warned the UK was underestimating the "technical difficulties" of Brexit. He said it will take a "huge amount of time" to reach agreement.

He highlighted the question of the rights of EU nationals in the UK and British expats in Europe, warning that it is in fact "a cortege of 25 different questions".

Juncker challenged May to sign a ready-made text on affected citizens' status, drafted by the Commission and its chief negotiator Michel Barnier, but admitted he did not think she would.

Addressing a press conference at the European Council summit in Brussels, Juncker said: "I have the impression sometimes that our British friends, not all of them, do underestimate the technical difficulties we have to face.

"A single and not simple question of citizens' rights is in fact a cortege of 25 different questions which have to be solved.

"So this will take time and if we want to be precise and to deliver guarantees to citizens, this will take a huge amount of time."

The guidelines set out that Brexit talks will agree the rights of EU citizens living in the UK, as well as Britons living in the EU, plus a settlement for the UK's financial obligations as an EU member state.

A deal must also be agreed to avoid a hard border between the Republic of Ireland and Northern Ireland. The deadline for completing the negotiations is March 29 in 2019.

However, Luxembourg's prime minister Xavier Bettel accused the Prime Minister of attempting to cherry-pick a Brexit deal.

He said: "Before you had the soft Brexit and the hard Brexit, and in future maybe you will have Theresa's Brexit, so maybe that is the reason she organised the elections."

Scotland's Brexit secretary Michael Russell welcomed the interventions from EU leaders.

He said: “There should be no illusions about the magnitude of the task ahead – and the EU has today made it clear that there will be no discussion on the UK’s future trading relationship with Europe until other key issues are resolved.

“Those issues include the status of EU citizens living in the UK, which Theresa May should resolve without further delay by guaranteeing their residency status."

UK Brexit Secretary David Davis, in response, said: "There is no doubt that these negotiations are the most complex the UK has faced in our lifetimes. They will be tough and, at times even confrontational".