UK and EU still disagree on citizens' rights: British Secretary of State for Exiting the European Union David Davis

Brexit Secretary David Davis (L) and Czech Foreign Minister Lubomir Zaoralek react during a press conference on July 25, 2017 in Prague, Czech Republic. (AFP photo)

British Secretary of State for Exiting the European Union David Davis has said there is a "moral imperative" to reach a quick deal on the rights of EU nationals living in Britain and UK citizens in the bloc.

The British government took "very, very seriously" the need to end the anxiety and uncertainty of both sides, Davis said at a news conference after talks with Czech Foreign Minister Lubomir Zaoralek in Prague.

"We want to do this quickly as a moral imperative because we want to take away the anxiety of all of those four million people and give them some certainty in their future," he said.

However, Davis again signaled that he is not willing to compromise over the role of the European Court of Justice (ECJ) and said British courts should be responsible for the rights of EU citizens in the UK after Brexit.

The biggest point of difference is Britain's insistence that the ECJ should not be involved in disputes that may arise after Brexit.

Brussels wants the rights of more than three million Europeans already in the UK to be protected by recourse to the ECJ. London opposes this, saying that any deal to protect EU citizens be accompanied by mutual guarantees for 1.2 million Britons on the continent.

Davis said UK courts are "trustworthy" and emphasized that the role the EU wants for the ECJ is rarely, if ever, seen elsewhere in the world.

"When we, for example, sign a deal, let's say with the United States, we don't give the United States Supreme Court the right to enforce that," he said.

On Tuesday, the European Parliament’s Brexit negotiator Guy Verhofstadt said the ECJ "must play its full role" and criticized the UK's approach to the Brexit negotiations.

UK and EU negotiators held their first full round of Brexit talks last week. The European Union’s chief Brexit negotiator Michel Barnier said Thursday that both sides had "fundamental" differences remaining.