Theresa May has admitted she had “robust” discussions with Jean-Claude Juncker during today’s EU summit in Brussels.
The prime minister and the European Council President were caught on camera locked in a heated row earlier on Friday.
Asked whether he had criticised her for being “nebulous” in her approach to the Brexit talks, May said he had been talking about “the general level of debate”.
“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,” she told a press conference.
Hitting back at Juncker, May also insisted she was “crystal clear” to EU leaders about the assurances about the temporary nature of the so-called Irish backstop she needs to get her deal passed by MPs, who fear being trapped in the arrangement.
Later on Friday, Juncker insisted he was not referring to May, and was instead describing the “overall state of the debate in Britain” as nebulous.
He added: “I was not addressing her, and in the course of the morning after having checked what I said yesterday night, she was kissing me.”
But he warned British MPs: “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. We have to bring down the temperature.”
Having survived a no-confidence challenge from her own MPs in Westminster on Wednesday, the prime minister had a bruising Thursday night in Brussels where her plea for meaningful changes to the Brexit deal was rejected by EU leaders.
And in a sign of rising tensions, May and the European Commission president could be seen having a tense conversation.
It comes after Juncker told reporters that May’s withdrawal agreement, which includes the controversial backstop plan, was not up for renegotiation, meaning MPs are likely to block the deal in a January parliamentary vote.
He said: “We don’t want the UK to think there can be any form of renegotiation, that is crystal clear.
“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.”
At the close of the summit on Friday, some leaders attempted to mount a rescue mission for May after she endured a difficult summit.
European Council president Donald Tusk said: “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.
“My impression is that in fact we have treated Prime Minister May with much greater empathy and respect than some British MPs, for sure.”
Austrian chancellor Sebastian Kurz also challenged media accounts of Thursday’s meeting between Mrs May and the EU27 leaders.
“Not all rumours in the media really go in line with how the meeting was,” said Mr Kurz.
“The problem is just that we have two different positions, but that’s all. Theresa May was I think a tough negotiator in the meeting and also made her point very clear.
“On the other side, the EU27 were united - which is good - and were able to make our point clear.
“I think not all the rumours about the meeting are probably true.”
Labour’s Brexit spokesman Keir Starmer, meanwhile, has called for May to move on and put the deal to MPs. He said: “It seems that the prime minister has failed in her bid to deliver meaningful changes to her Brexit deal.
“We cannot go on like this. The prime minister should reinstate the vote on her deal next week and let Parliament take back control.”