- Video report by ITV News Europe Editor James Mates
Donald Tusk has hit out at British MPs, saying the EU has treated Theresa May with "more respect and empathy" than many in her own government.
Taking aim at British politicians, European Council president Mr Tusk said: "We have treated prime minister May with the greatest respect - all of us."
Joining Mr Tusk at a press conference on Friday was Jean-Claude Juncker, who earlier was filmed in a tense conversation with Mrs May after EU leaders rejected her attempts to win fresh concessions for her Brexit deal.
Mr Tusk said: "My impression is that in fact we have treated prime minister May with much greater empathy and respect than some British MPs, that's for sure."
European Commission president Mr Juncker also praised Mrs May, describing her as a "woman of great courage" who is "a good friend of ours".
In an earlier press conference, Mr May said she had had a "robust" discussion with Mr Juncker after she appeared to have taken particular issue with a description of her presentation to EU leaders on Thursday as "nebulous", meaning vague or ill-defined.
- Video report by ITV News Political Correspondent Libby Wiener
Brushing off the incident in a press conference, which ended the two day EU summit, Mr Juncker said he had not been "addressing her", adding jokingly, "and in the course of the morning after having checked what I said yesterday night, she was kissing me."
Mrs May said that following her discussion with the EU Commission President, she accepted "he'd been talking about a general level of debate".
Mrs May had gone to Brussels seeking a way to get the Withdrawal Agreement through a heavily divided Commons, insisting she could do it but had to be able to convince MPs the UK would not find itself tied to the EU indefinitely through the Northern Ireland "backstop".
But her proposals were rebuffed, with Mr Juncker criticising a lack of clarity over what she was seeking from the future relationship.
ITV News Political Editor Robert Peston said one observer of the conversation between May and the EU27 leaders on Thursday said the prime minister "could not say what would actually deliver a majority in Parliament for her”.
- Watch Theresa May's exchange with Jean-Claude Juncker:
- And this is what the PM had to say about it:
"Our UK friends need to say what they want, instead of asking us to say what we want," Mr Juncker said.
"So we would like, within a few weeks, our UK friends to set out their expectations for us because this debate is sometimes nebulous and imprecise and I would like clarifications."
He added: "We don't want the UK to think there can be any form of renegotiation, that is crystal clear. We can add clarifications but no real changes.
"There will be no legally binding obligations imposed on the withdrawal treaty."
On Friday, Mrs May said she had been "crystal clear" to EU leaders at the Brussels summit about the need for assurances on the backstop in response to MPs' concerns.
Asked about her conversation with Mr Juncker, she said: "I had a robust discussion with Jean-Claude Juncker - I think that's the sort of discussion you're able to have when you have developed a working relationship and you work well together.
"And what came out of that was his clarity that actually he'd been talking - when he used that particular phrase - he'd been talking about a general level of debate."
Mrs May welcomed commitments by the EU27 to try to get a new trade deal completed quickly enough that the backstop would not be needed, and said that as formal conclusions from the summit they had "legal status".
But she said that it was clear that "further clarification and discussion" is possible.
Mrs May said it was in the interests of the EU and UK to "get this over the line", warning: "A disorderly Brexit would be good for no-one."
Earlier Irish premier Leo Varadkar said all EU leaders see the Irish border backstop as vital to protect the integrity of the European single market.
Mr Varadkar said he was "very satisfied" with the summit conclusions on Brexit which made clear the withdrawal agreement was not "up for renegotiation".
The EU hardball approach appears to leave Mrs May with limited room for manoeuvre during the countdown to the UK's departure on March 29.
The prime minister, who on Wednesday survived a bruising vote of no confidence by Tory MPs, said a package of assurances around the backstop could "change the dynamic" at Westminster.
At the same time, she made clear that a failure by EU leaders to offer concessions risked the collapse of the whole agreement, with the UK leaving in March in a disorderly, no-deal Brexit.
DUP leader Arlene Foster said the reaction of the EU to Mrs May's appeals for help was "unsurprising" but was insistent she wanted to see the "backstop fundamentally changed".
She told ITV News: "At the moment it separates Northern Ireland off from the rest of the United Kingdom, in a constitutional fashion and in an economic way as well. So therefore we need to be able to see the backstop go and she has to deal with the backstop in a meaningful way."
"The prime minister knows what is needed to achieve the consensus of parliament. She needs to have those legally binding changes to the Withdrawal Agreement and of course we want to see her achieving that."
Ms Foster said the DUP could not support the deal as it currently stands.
"We did warn the prime minster many months ago not to go down this road. She decided to go down this road and now we're in the situation we're in today."
She added she did not support no Brexit or a suspension of Article 50, saying it was simply pushing the the issues "further down the road".