Theresa May has said it is still possible to get the assurances MPs need to back her Brexit deal, despite EU leaders ruling out any renegotiation.
At a summit in Brussels, the UK PM said there was “work to do” but talks on “further clarification” would continue.
She admitted a “robust” discussion with European Commission President Jean-Claude Juncker, after he complained about “nebulous and imprecise debate”.
Labour said the withdrawal deal was now “dead in the water”.
Pooled video footage of Mrs May and Mr Juncker captured a tense exchange on Friday morning after his remarks the previous night.
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.
BBC political editor Laura Kuenssberg said for the PM to say she had had more talks and reassurances “doesn’t change the fact that she’s going home, seemingly empty handed, at a moment of huge vulnerability”.
If this meeting was meant to provide Theresa May with the beginnings of an escape route from her Brexit conundrum, the signs are nothing less than awful.
At one of her most vulnerable political moments, Number 10 was hopeful at least of an indication of a potential solution to the most intense of a long list of Brexit problems – the controversial so-called backstop, designed to guarantee there would be no hard Irish border.
But right now, that’s simply not on offer.
EU leaders made it plain that their warnings – that their divorce deal with Britain was not up for negotiation – were real.
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 “speedily” so that the backstop would not be needed.
She said that, as formal conclusions from the summit, they had “legal status” but added: “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.”
On Thursday evening, European Council president Donald Tusk said the withdrawal agreement was “not open for renegotiation” while Mr Juncker said: “Our UK friends need to say what they want, instead of asking us to say what we want, and 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.”
Mrs May said she had held discussion with both on Friday and added: “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.”
‘Dead in the water’
But Labour leader Jeremy Corbyn said: “The last 24 hours have confirmed that Theresa May’s Brexit deal is dead in the water. The prime minister has utterly failed in her attempts to deliver any meaningful changes to her botched deal.
“Rather than ploughing ahead and dangerously running down the clock, the prime minister needs to put her deal to a vote next week so Parliament can take back control.”
And Conservative Brexiteer Mark Francois told the BBC: “It is as plain as a pikestaff that this will never get through the House of Commons… the prime minister, I’m afraid, is completely boxed in.”
The Democratic Unionist Party, on whom Theresa May relies for her Commons majority, urged Mrs May not to “roll over as has happened previously” and to “stand up to” the EU.