"We have had cross-party discussions initiated finally with Labour by [UK Prime Minister] Theresa May. We all expressed our hopes and expectations in this regard… our expectations and our hope that this dialogue will conclude with a positive result, which will allow us at last to have a positive majority emerge with regard to this withdrawal agreement… This cross-party dialogue is the new element which could lead to a request, which we would be then willing not only to agree to but also to implement for our future relations," Barnier told reporters after a General Affairs Council on Article 50.
Barnier has further stressed that the European Union would be willing to amend the political declaration on future ties rapidly.
The UK prime minister has asked the European Union for a second short Brexit extension, this time until 30 June, as the first one, until 12 April, has not resulted in the deal approval in the UK parliament.
A special session of the European Council on Brexit will be held on Wednesday, and May is meeting French president Emmanuel Macron and German Chancellor Angela Merkel ahead of the meeting, on Tuesday.