Prime Minister Theresa May has insisted she was "crystal clear" to EU leaders at the Brussels summit about the need for assurances on the Irish border backstop in response to MPs' concerns.
She 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 discusssion" is possible.
Mrs May said she had a "robust" discussion with Jean-Claude Juncker after she was asked about footage showing her speaking to the European Commission president.
The Prime Minister 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 said: "The EU is clear, as I am, that if we are going to leave with a deal, this is it.
"But my discussions with colleagues today have shown that further clarification and discussion following the council's conclusions is in fact possible.
"There is work still to do and we will be holding talks in coming days about how to obtain the further assurances that the UK Parliament needs in order to be able to approve the deal."
Following reports that European Commission president Mr Juncker had described her presentation to EU leaders on Thursday as "nebulous", Mrs May said: "I was crystal clear about the assurances that were needed on the backstop, having heard the views of MPs in the House of Commons."
She 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."
She said that the EU27 conclusions made clear that the EU is determined to work speedily on a future relationship - or alternative arrangements - to ensure by the end of 2020 that there will be no hard border in Ireland, so that the backstop need not be triggered.
The conclusions confirm that any backstop would be temporary and that, if it was ever needed, the EU would negotiate "expeditiously" an agreement to put a replacement in place.
She said: "As formal conclusions, these commitments have legal status and therefore should be welcomed."
But she said she had discussed with EU leaders, including Mr Juncker and Council President Donald Tusk, the fact that MPs would require "further assurances".
She said: "It is in the overwhelming interest of all our people in the EU and the UK to get this done and as quickly as possible."
Mrs May managed a smile when a reporter asked if she had had a "trying week", jokingly replying: "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.
She added: "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."