Theresa May and Jean-Claude Juncker have met in Brussels and described their talks on changing the Brexit deal as "robust but constructive"
In a joint statement, the European Commission President stressed the withdrawal agreement could not be changed, as the UK PM wants.
But he said the EU was open to adding words to the non-binding future relations document that goes with it.
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In a statement talks are set to resume to see "whether a way through can be found that would gain the broadest possible support in the UK Parliament and respect the guidelines agreed by the European Council".
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"Despite the challenges, the two leaders agreed that their teams should hold talks as to whether a way through can be found that would gain the broadest possible support in the UK Parliament and respect the guidelines agreed by the European Council.
"The Prime Minister and the President will meet again before the end of February to take stock of these discussions."
Brexit Secretary Stephen Barclay and EU negotiator Michel Barnier will hold talks in Strasbourg on Monday.
The statement said Mrs May "raised various options" for dealing with MPs' concerns about the backstop.
"The Prime Minister described the context in the UK Parliament, and the motivation behind last week's vote in the House of Commons seeking a legally-binding change to the terms of the backstop.
"She raised various options for dealing with these concerns in the context of the Withdrawal Agreement in line with her commitments to the Parliament."
Mr Juncker "underlined that the EU27 will not reopen the Withdrawal Agreement" but "expressed his openness to add wording to the Political Declaration agreed by the EU27 and the UK in order to be more ambitious in terms of content and speed when it comes to the future relationship".
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