This comes in the wake of the breakdown in talks over the Irish border issue between UK Prime Minister Theresa May and top EU officials in Brussels on Monday.
Talks with European Commission President Jean-Claude Juncker broke up without agreement on Monday, although both sides said they were hopeful of getting a deal by the end of the week.
May is under pressure to get an agreement from the Democratic Unionist Party (DUP) on the status of the Irish border when the UK leaves the EU.
The Prime Minister pulled out of a deal with Brussels that would have kick-started trade talks after meeting fierce resistance from the DUP.
The party said it would not accept a deal which saw Northern Ireland treated differently from the rest of the UK. She will return to Brussels as early as Wednesday to try again.
May was due to update ministers at a cabinet meeting on Tuesday morning.
Parliament’s EPP group leader Manfred Weber warned that lawmakers were not yet satisfied.
“On Brexit negotiations, money is one of the problems, but it is not the biggest one. We are much more concerned about the fact that so far negotiations are stalled on the protection of EU citizens’ rights after Brexit and on the Irish case,” he said.
Parliament’s ALDE group leader Guy Verhofstadt, a member of parliament’s Brexit steering group, said that he and his colleagues wrote to the EU negotiators last week to sound an alarm at what they said were “stalled” talks on EU demands that the rights of EU citizens in Britain be guaranteed directly by the European Court of Justice after Britain leaves the EU. They also voiced concern about Northern Ireland, he said.
Addressing another of the EU’s three Brexit red lines, citizens’ rights, Verhofstadt added, “During my meeting with Juncker, I reiterated that EU citizens in the UK should not have to go through an unclear, costly and burdensome procedure. Their rights must be guaranteed. They came to the UK in good faith.”
S&D group Chair Gianni Pittella said, “No deal, but still some positive progress in Brexit negotiations. We fought hard to protect rights of EU citizens and their families. The possible continued alignment of Northern Ireland with EU rules could be a crucial turning point in the negotiations.”
Further reaction came from Simon Coveney, Ireland’s deputy Prime Minister, who said, “We have been moving forward on the basis of good faith. We believe the British government has also been. There has been very difficult negotiations, we recognise these are very difficult political issues to manage for the British prime minister and we want to give her the time and the space to do that.
“But we don’t want to give the impression the Irish government is going to reverse away from the deal we felt we had in place and agreed yesterday.
“Of course, it there are presentational issues they want to work with we will look at that.”