The demand was made by several MEPs, including ALDE group leader Guy Verhofstadt who were speaking in a debate in parliament in Strasbourg on Wednesday.
The debate comes on the eve of an EU summit on Thursday where EU leaders are expected to signal that sufficient progress has been made in the Brexit talks with the UK government to proceed to the second phase early in the New Year.
Verhofstadt told MEPs meeting in plenary that he had spoken to David Davis, the UK’s chief Brexit negotiator on Tuesday. “I spoke to [David Davis] on the phone and he assured me it is not his intention or the UK government’s intention to backtrack on the commitments given last Friday.”
“If that is the case then the best thing in the coming weeks is to transpose these commitments made last week into a legally binding text. That is the best way forward.”
Verhofstadt said there are still issues to be resolved on the EU’s red lines, including on citizens’ rights.
“We need legal protection for British citizens living in the EU. We in the EU seem to care more about this than the whole British government. [The European] Parliament cannot give a green light to a formal agreement unless these conditions are met,” he said.
On the Irish border issue, he said Ireland “cannot become the collateral damage of Brexit.”
The Belgian MEP and former prime minister is the European Parliament’s chief Brexit negotiator.
"The best thing in the coming weeks is to transpose these commitments made last week into a legally binding text. That is the best way forward” Guy Verhofstadt
On citizens’ rights, the leader of the Parliament’s Socialist group Gianni Pittella said, “Protecting EU citizens and their families must be a priority.”
British Conservative MEP, Syed Kamall, said, “We are now looking to the future and the deal is a positive step. Not everyone got what they wanted but, as many of us who know the realities of trying to find a deal, compromises are needed and both sides.
“I know there are large number of people in [this] parliament who had wished for a different referendum result but my message to them is that Brexit will not change our common interests.
“I hope Theresa May and Donald Tusk have laid the first foundations for the future ahead and for a trade agreement where both the UK and EU cooperate.”
Gabriele Zimmer, the leader of Parliament’s GUE group, said, “The recent behaviour of the UK government has not instilled trust and confidence and there is a need to act on citizens’ right as we are very concerned about family reunion, the future of children and couples. We want full recognition of professional qualifications and health access. These have to be maintained and not watered down or reduced.
“I know there are large number of people in [this] parliament who had wished for a different referendum result but my message to them is that Brexit will not change our common interests" Syed Kamall
“We have to take it upon ourselves to be the guarantor of the rights of British citizens in the EU.”
Greens/EFA co-leader Ska Keller said, “The question of Northern Ireland remains a crucial issue for us. Theresa May's assurance that there will not be a hard border between Northern Ireland and the Republic of Ireland is promising, but it is not a solution.
“The remarks from British Brexit Minister David Davis, who described the agreement as merely a non-binding "letter of intent", certainly don't inspire confidence. We will not agree to any deal with the United Kingdom that threatens peace in Northern Ireland.”
Further comment came from UKIP MEP Nigel Farage who said, “I don’t think I’ve ever heard so little criticism of the United Kingdom in this chamber in all my life, I guess that doesn’t really take much working out does it?”
“Theresa the appeaser has given in on virtually everything.”
“Theresa the appeaser has given in on virtually everything” Nigel Farage
“We’re volunteering to go on paying the membership fee, to accepting all the existing rules, all the new rules, we will effectively once the transition is granted have left the European Union at the end of March 2019 in name only.”
He cited the “ludicrous divorce bill, the continued role of the European Court of Justice and “open door immigration from the EU.”
“The EU made a UK prime minister leave Downing Street in the middle of the night to fly to Brussels and agree a deal with a bunch of unelected officials.
“[Theresa] May has been subjected to ritual humiliation and to dance to the tune of the EU. We will have left the EU in 2019 but in name only. So I understand why so many here feel encouraged by our PM and also why so many who voted for Brexit feel mounting anger. I fear that Brexit may need to be re-thought all over again.”
Further comment came from Diane Dodds, a British non-attached member, who said, “We share the goal of no hard border in Ireland but this can only be dealt with in phase two. However, our main concern is trade between the UK and Northern Ireland.”
“Brexit is a lose-lose situation for both the UK and EU and that is why Donald Tusk must offer the UK a new deal which avoids Brexit" Hans-Olaf Henkel
Elmar Brok, a centre-right member from Germany, said, “Let’s be clear: an agreement has been reached under which we hear Britain is a supplicant. But the UK government has made commitments which need to be fleshed out in a final agreement. If Farage says those in the EU are unelected officials then the only unelected party in the UK is his own as it has no elected MPs.
“There has to be confidence and trust in these talks. We do not want this to be destroyed by discussions in the UK.
Liberal group deputy Roberto Gualtieri said, “Despite some propaganda I am confident this deal will safeguard the rights of citizens affected by Brexit.”
Hans-Olaf Henkel, of the European Conservatives and Reformists Group, said, “To map out a trade deal with Canada is one thing but to do so with a country we have had relations with for 40 years is another thing altogether.
“We are losing, possibly an important trading partner, but also 73 British MEPs.”
He added, “Brexit is a lose-lose situation for both the UK and EU and that is why Donald Tusk must offer the UK a new deal which avoids Brexit. At present, the two side are like two trains heading in the same direction and Brexit will be a catastrophe. The EU will never be competitive without the UK.”
Sophia in 't Veld, of the Group of the Alliance of Liberals and Democrats for Europe, told the plenary debate, “Sufficient progress has not been made, including on citizens’ rights. Mrs May promised to create a hostile environment and she has been successful.”