The European Parliament's Brexit group has said it would not approve a withdrawal agreement that did not contain a "backstop" provision to avoid a hard border in Ireland.
The parliament's Brexit Steering Group, chaired by Guy Verhofstadt, "reiterated that the withdrawal agreement is fair and cannot be re-negotiated. This applies especially to the backstop ... without such an 'all-weather' backstop-insurance, the European Parliament will not give its consent to the withdrawal agreement."
The European Parliament must give its consent to any final Brexit deal between the EU and the UK.
"The EU remains clear, firm and united on this even if the negotiated backstop is not meant to be used," the Brexit Steering Group statement said.
Earlier, the EU's chief negotiator, Michel Barnier, said that backstop could not be time-limited
He also insisted it would be "legally impossible" for the UK to forge a separate treaty with Ireland to govern the border following EU withdrawal.
Speaking to Germany's Deutschlandfunk radio during a visit to Berlin for talks with Chancellor Angela Merkel this morning, Michel Barnier restated his position that there can be no time limit on the proposed backstop arrangement to keep the border open after Brexit.
"Such insurance cannot be limited," said Mr Barnier.
"Imagine that you have house insurance and it suddenly becomes temporary. Nobody would sign up for that. And then at some point a misfortune happens and you have no insurance. No, this insurance may not be limited in time."
Mr Barnier said that "self-evidently" the EU would have to be able to conduct checks on goods coming from Northern Ireland after Brexit, but said that Brussels remained committed to avoiding a hard border.
The solidarity of the EU27 with Ireland will remain "steadfast" throughout remaining negotiations, he added.
And he brushed off any separate deal between the UK and Ireland: "What you are proposing here is legally impossible, because this border between the United Kingdom and Ireland is not only a border between the two countries, but it is the border with Germany, it is the border with France, with the Netherlands, with Poland, and indeed with the entire internal market.
"No, legally it is not possible to separate that from each other."
Mr Barnier also said that Brexit would be "bumpy" if the UK Parliament failed to come together behind a deal.
"What we have now is a double majority against the deal on the one hand and against the no deal on the other," he said.
"But we need something that is positively accepted as an agreement."
In a message to MPs, he said: "In order to avoid this difficulty of leaving without an agreement, this no-deal, it is not enough to vote against the no-deal. No, you have to vote for a contract, an agreement.
"If nothing moves, if no positive suggestions are put on the table, then we will be heading for a more or less bumpy or accidental no-deal on March 30."
He added: "I hope now that in this dialogue with the parties of her country which she has begun, both with her own majority and with the opposition parties, Mrs May will find a way to find a positive majority in support of this treaty to start an orderly withdrawal."
Mr Barnier played down suggestions that the two-year Article 50 process ought to be extended to allow more time for negotiations, saying: "I personally believe that we do not need so much more time, but that we now need to make decisions, to be taken by the British government and the Parliament of Great Britain."
He said the EU would respond if Theresa May amended her "red lines", which include leaving the customs union and single market and the jurisdiction of the European Court of Justice.
"If anything moves on the British side with those red lines, yes, then we're ready to talk about it," he said.
"I hope this happens, and that is possible."
Additional Reporting Reuters