AN exasperated Theresa May has publicly slapped down Jean-Claude Juncker after they were caught on camera having a diplomatic spat, which she described as a “robust discussion”.

In a press conference, which was delayed for almost 100 minutes, the Prime Minister insisted she had been “crystal clear” about the need for further assurances from the EU27 on the Irish backstop in response to MPs' concerns.

READ MORE: EU leaders tell Theresa May Brexit withdrawal agreement is 'not open for renegotiation' 

But earlier as the EU leaders sat down for the start of the second day of the EU summit discussions, a TV camera caught Mrs May confronting the European Commission President over remarks he was said to have made the night before when he described the UK’s approach as “nebulous”.

In a late night press conference on Thursday, Mr Juncker took the UK Government to task for its lack of clarity, saying it was time for it “to say what they want instead of asking us to say what we want”.

But this morning the PM, clearly aware the camera was filming her exchanges, told the Commission President that he had described her approach as nebulous. “Yes, you did,” she declared.

Taking her by the elbow, Mr Juncker replied: “No I didn't. I didn't." Finally, it was left to Mark Rutte, the Dutch premier, to intervene to calm things down as the camera panned away.

The incident underlined the tensions surrounding the latest talks after EU leaders rejected the PM’s attempts to win fresh concessions to the agreed Brexit deal, namely, to get a legally-binding addition to the Withdrawal Agreement that would empower Britain to leave the Irish backstop under its own terms.

At the press conference, Mrs May was asked about her public spat with the Commission President and replied: “I had a robust discussion with Jean-Claude Juncker.

“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."

Earlier, she told reporters that it was in the “overwhelming interest of all our people” in the EU and the UK to “get this over the line”. She stressed: “A disorderly Brexit would be good for on one.”

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The PM explained how it was the EU27’s “firm determination to work speedily on the future relationship or alternative arrangements, which ensure no hard border by December 2020, so the backstop will not need to be triggered”.

If it were triggered, it would apply only temporarily and the EU27 would use its “best endeavours” to “conclude expeditiously” a subsequent agreement that would replace the backstop and that the EU stood ready to embark on preparations so that negotiations on the future partnership would start as soon as possible

Mrs May insisted further clarifications from the EU27 were possible and she would hold further talks in the coming days to get further assurances so that MPs could approve the deal.

At the end of a bruising few days, the PM managed a smile when a reporter asked if she had had a "trying week". She replied jokingly: "Has something happened this week?"

When asked whether the problems with her party at home and dealing with the EU had made her want to quit as leader, she said it was "our duty as a Government and as a Parliament" to see Brexit through.

Mrs May explained: "I never said it was going to be easy. Negotiations like this are always tough. There are always difficult times and as you get closer to the very end that can get even more difficult because you are sorting out the last details of something."

She added: “What drives me to carry on doing this and making sure we deliver is that this is what’s right for the British people. What we are going to see out of this is not just us outside the EU but also that we’re able to take advantages that gives us in building that brighter future for Britain.”

On Thursday during his late night press conference, Mr Juncker made clear: "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."

This morning Leo Varadkar, the Irish premier, said he was "very satisfied" with the summit conclusions on Brexit which made clear the withdrawal agreement was not "up for renegotiation".

He added: "It is very much a case of the European Union being one-for-all and all-for-one."

But the Democratic Unionists' Arlene Foster called on Mrs May to stand up to her fellow European leaders and demand changes to the Withdrawal Agreement.

The DUP leader, whose party is keeping the UK Government in power through a confidence and supply deal at Westminster, has vowed to vote against the draft treaty if the contentious Irish border backstop was not binned.

"The Prime Minister has promised to get legally binding changes. The reaction by the EU is unsurprising. They are doing what they always do. The key question is whether the Prime Minister will stand up to them or whether she will roll over, as has happened previously,” declared Ms Foster.

"This is a difficulty of the Prime Minister's own making. A deal was signed off which the Prime Minister should have known would not gain the support of Parliament.

"If the Prime Minister had listened to our warnings and stood by her public commitments, we would not be in this situation," she added.

At Westminster, Labour’s Sir Keir Starmer called for a meaningful vote on the deal before Christmas; No 10 has made clear it is now planned for January.

"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," added the Shadow Brexit Secretary.

One option, which some Cabinet ministers are said to be favouring, including Chancellor Philip Hammond, Work and Pensions Secretary Amber Rudd, and David Mundell, the Scottish Secretary, is that, if Mrs May’s deal does not get through, then Parliament should have non-binding indicative votes on the range of options, including a Norway-plus option, the Canada trade deal option and a no-deal scenario.