Taoiseach Leo Varadkar and British Prime Minister Theresa May at the meeting in Brussels.
PHOTO: REUTERS/YVES HERMAN
"Negotiations like this are always tough, there are always difficult times and as you get close to the very end, then that can get even more difficult because you're absolutely sorting out the last details of something," May said.
She added that the current deal is in the best interests of the EU and the UK and said it would be better to leave with a deal.
Mrs May also addressed an animated conversation she had with President Jean-Claude Juncker earlier in the day.
May had earlier been filmed on an official video remonstrating with Juncker at an EU summit in Brussels where she appeared to be accusing him of labelling her nebulous, a term he used on Thursday to describe the debate around Brexit.
"I had a robust discussion with Jean-Claude Juncker," she told reporters. "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 he had been talking, when he used that particular phrase, ... about a general level of debate."
EU leaders have warned Theresa May she cannot expect a "legally binding" commitment that the UK will not be tied to the bloc indefinitely through the Northern Ireland backstop.
The British Prime Minister went to Brussels to appeal to the leaders of the 27 to give her the assurances that would enable her to get her Brexit deal through Parliament.
But while they promised to do their utmost to ensure the backstop - intended to ensure there is no return to a hard border between the North and the Republic - was never needed, they insisted they could not re-open the terms of the Withdrawal Agreement.
European Commission president Jean-Claude Juncker said: "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."
It is a significant blow to Mrs May who had sought legal assurances that the backstop will be temporary.
EU leaders also deleted a reference in draft text to being "ready to examine whether any further assurance can be provided".
And the Taoiseach insisted the Border backstop "is not on the table" as part of renewed efforts to get Brexit over the line.
Leo Varadkar said the backstop would protect Irish interests in the immediate crux - and in any future talks on a big-picture EU-UK trade deal after Brexit.
Mr Varadkar, who had earlier met Mrs May, said efforts to get the London parliament to ratify a deal would centre on "explanations, assurances and clarifications".
For the moment, the assurances are political but the Taoiseach notably did not rule out some kind of legal device.
Mr Varadkar's meeting with Mrs May was supposed to happen in Dublin on Wednesday but had to be postponed amid high political drama in London. Though Mrs May beat a no-confidence motion tabled by her Conservative Party colleagues, the draft Brexit Withdrawal Agreement remains as far away as ever from the necessary approval of her MPs.
The Taoiseach insisted all EU leaders were totally agreed that the EU-UK deal cannot be re-opened in efforts to overcome British lawmakers' hostility.
But every effort would be made by the EU to help the UK MPs understand and hopefully support the draft deal.
"I can tell you the backstop is not on the table. It needs to be there for a number of reasons," the Taoiseach said.
"It needs to be there to give us the assurance that there will be no hard Border between Ireland and Northern Ireland, thus protecting the peace process and the Good Friday Agreement," he continued.
"It needs to be there for European reasons as well, giving Europe the assurance that the open Border will not become the backdoor to the single market," the Taoiseach added.
Mr Juncker also criticised the UK's lack of clarity over the future relationship it is seeking with the EU once it has left.
"Our UK friends need to say what they want, instead of asking us to say what we want," he 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."
The rebuff came after Mrs May - who survived a bruising vote of confidence by Tory Mps - told EU leaders that she could get a Commons majority for the controversial deal, despite heavy criticism from all sides of the House.
However, in a meeting with the leaders of the remaining 27, she said she had to be able to convince MPs the UK would not find itself tied to the EU indefinitely through the "backstop".
"There is a majority in my Parliament who want to leave with a deal so with the right assurances this deal can be passed," she said in prepared remarks released by No 10.
"Indeed it is the only deal capable of getting through my Parliament."
She made clear 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.
"We have to change the perception that the backstop could be a trap from which the UK could not escape. Until we do, the deal - our deal - is at risk," she said.
"It is in none of our interests to run the risk of accidental no-deal with all the disruption that would bring, or to allow this to drag on any further."
After listening to her appeal, European Council president Donald Tusk said EU leaders had reaffirmed that the backstop was intended as an "insurance policy" to prevent the return of the hard border.
He said that they had expressed a "firm determination" to work "speedily" to ensure there was an agreement on the future relationship in place by the end of the transition period in December 2020 so the backstop was not needed.
He said that if the backstop was ever activated it would apply temporarily "unless and until it is superseded by an agreement" that ensures a hard border between Northern Ireland and the Republic is avoided.
However such assurances are likely to cut little ice with critics of the agreement who have been demanding a "break clause" to ensure the UK cannot be held in the backstop indefinitely.