German Chancellor Angela Merkel has said that the EU's Withdrawal Agreement with the UK is not up for renegotiation.
It comes after British Prime Minister Theresa May acknowledged that it would not be possible to reopen the agreement to alter the backstop provisions which have sparked mass rebellion among Tory MPs.
As a result, Britain is to have talks with the EU over the coming days about how to obtain "further assurances" which might persuade MPs to back the Brexit Withdrawal Agreement, Mrs May said.
In a press conference at the conclusion of the summit, Chancellor Merkel said that the EU27 had told Mrs May it was "important for us that the future relationship between the EU and the UK should be a relationship in which each partner can freely develop".
The Chancellor said: "We want a close relationship with Great Britain. We have also been clear as to the extent that we only see the backstop as a kind of insurance should we not succeed in negotiating a final agreement about our future relationship within the transition period.
"We address ourselves again to Great Britain, indicating that the EU27 do not want us to stay in the backstop period for a long time. Rather, we would not want it to be applied at all. We want it - if it has to be applied - to be as short as possible.
"All the 27 want to make sure it is not a disorderly Brexit. These are the assurances we have given to the British Prime Minister. Now we await her response."
Mrs Merkel added: "We want to be helpful, but within the framework I have been describing. We don't want to amend the Withdrawal Agreement and we will have to continue to work on the future relationship anyway. So we have explained that to Theresa May."
Asked whether the EU would be prepared to offer further reassurance to Mrs May, Mrs Merkel said: "The 27 member states have given assurances. They are contained in the conclusions of yesterday evening.
"That is our position. That is what we have put on the table. And now we expect Great Britain to respond."
Mrs Merkel declined to say how she would respond if the UK were to vote to remain in the EU in a second referendum, saying: "That is total speculation. I never respond to total speculation."
The Chancellor added: "You know that we are all preparing for the eventuality of a disorderly Brexit, which is something we will be working hard to prevent from happening."
European Commission president Jean-Claude Juncker told reporters Mrs May was a "good friend", adding: "I admire her because this is a woman of great courage doing her job in the best way possible.
"I am supporting her, not as far as all the content elements are concerned, but I am supporting the way she is dealing with that matter."
Mr Juncker went on to say that while the Withdrawal Agreement "will stay" as it is, the EU was ready to start talks on a future relationship as soon as it is ratified in an attempt to assuage doubts over the Irish border backstop.
He said: "We decided yesterday under the chairmanship of President Tusk that the second after an approval by the two parliaments, the British one and the European one, and before signatures, will start the negotiations on the future relations.
"Because I was following second by second the debate in the House of Commons and I noted there was a deep mistrust in the House when it comes to the European Union.
"That is not a good basis for future relations, but in order to prove that we mean this seriously the negotiation on future relations and we mean it seriously that we don't want to have this backstop being permanent, then we have to discuss and to start our negotiations."
"We have to bring down the temperature. These attacks coming from Westminster against Europe and the European Commission will not be responded to in the same way by Europe and the European Commission, although I would like to do it."
NEW - Two expert lipreaders tell 5 News that Theresa May accuses Jean-Claude Juncker of describing her as nebulous.
This is how the conversation went, according to the lipreaders: pic.twitter.com/IuP99fJiXG— Channel 5 News (@5_News) December 14, 2018
Mr Juncker said he was not referring to Mrs May in his "nebulous" comment.
Asked about the video clip of Mrs May confronting him, he said: "She thought that I did criticise her by saying yesterday night that the British position was nebulous... I did not refer to her but to the overall state of the debate in Britain.
Mr Juncker said: "Theresa May is a good friend of ours. We have the highest respect for the British Prime Minister, because she has to deliver a very difficult job."
Pointing to Mr Tusk, a former Polish PM, the long-serving ex-premier of Luxembourg said: "The two of us were prime minister and we sometimes had to face motions asking for our resignation."
And gesturing to Austrian Chancellor Sebastian Kurz, he joked: "It will happen to Sebastian in a short period of time.
"So we are sympathising with Mrs May.
"I have the highest respect for the British Prime Minister."
European Council president Donald Tusk said: "I would like to underline one thing after what I've read and what I've heard in some newspapers and TV stations.
"We have treated Prime Minister May with the greatest respect, all of us. And we really appreciate the efforts by the Prime Minister to ratify our common agreement.
Mr Tusk also said he has "no mandate" for renegotiating the Withdrawal Agreement, but said he would remain at Mrs May's "disposal".
He told the press conference: "Yesterday's conclusions are quite clear I think and we have to treat it as a good sign I mean that we are ready to reconfirm our assurances and our goodwill and good faith when it comes to so-called backstop.
"I have no mandate to organise any further negotiations - we have to exclude any kind of reopening our negotiations on the Withdrawal Agreement but of course we will stay here in Brussels and I am always at Prime Minister Theresa May's disposal."
- Digital Desk and PA