Prime Minister Theresa May has said there is still "work to do" to reassure MPs that the Brexit deal agreed with the EU but that it "is possible".
Speaking after EU leaders stressed the deal was "not open for renegotiation", she said she had discussed with them the need for "further clarification".
She admitted having a "robust" discussion with European Commission President Jean-Claude Juncker.
He urged more clarity from the UK after "nebulous and imprecise" debate.
Pooled video footage of the two of them caught a tense exchange on Friday morning after his remarks.
Mrs May told reporters: "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."
The UK prime minister travelled to Brussels to make a special plea to EU leaders after delaying Tuesday's Commons vote on the deal, in anticipation of a heavy defeat.
She then went on to win a confidence vote brought by her own MPs but vowed to listen to the concerns of the 37% of Tory MPs who voted against her.
Many of them are concerned that the controversial "backstop" plan in the withdrawal agreement Mrs May has negotiated, which is aimed at preventing a hard border in Northern Ireland, would keep the UK tied to EU rules indefinitely and curb its ability to strike trade deals.
Mrs May said she was "crystal clear" to EU leaders about the need for assurances on the backstop and welcomed commitments by other EU leaders to try to get a new trade deal in place quickly so that the backstop would not be needed.
She said that, as formal conclusions from the summit, they had "legal status" but also made clear that "further clarification and discussion" was needed.
"There is work to be done. It is clear we can look at this issue of further clarification. We will be working expeditiously over the coming days to seek those further assurances I believe MPs will need."