Theresa May says she has secured "legally binding" changes to her Brexit deal, a day ahead of MPs voting on it.
But European Commission President Jean-Claude Juncker warned if the deal was voted down there was "no third chance".
They spoke at a joint press conference in Strasbourg after a late meeting.
Labour leader Jeremy Corbyn said the prime minister's negotiations had "failed" and the announcements did not contain "anything approaching the changes" she had promised Parliament.
Cabinet Office Minister David Lidington announced the changes to the Commons shortly before the press conference, saying they would mean the EU "cannot try to trap the UK in the [Irish] backstop indefinitely".
Mrs May confirmed she would be opening the debate tomorrow ahead of a so-called "meaningful vote" on her deal, which must be agreed by Parliament to come into force.
Last time her deal was put to Parliament in January, she suffered an historic loss as it was voted down by a margin of 230.
The PM also said her attorney general, Geoffrey Cox, would publish his legal advice on the changes to the deal before the vote.
Downing Street had earlier said the PM's focus was "getting on with the work required to allow MPs to support the deal and to bring this stage of the process to an end".
The UK is due to leave the EU on 29 March but MPs rejected the withdrawal deal on offer in January and demanded major changes.
BBC Brussels reporter Adam Fleming said the mood had been "bleak" in Brussels after the EU's chief Brexit negotiator, Michel Barnier, briefed EU ambassadors on the state of play earlier.
Mr Fleming said the member states were told that the UK had rejected the EU's proposed solutions on the backstop because "they wouldn't get the support of the Cabinet".
"There is a widely held view that the UK has not been negotiating in good faith over the last few days," he said, adding that at least one diplomat had mentioned planning for a "post-Theresa May government".
The government has been seeking changes to the Irish backstop, the safety net designed to maintain an open border on the island of Ireland, and only to be used as a last resort.
But the details of it were a sticking point for many MPs when they voted her deal down in January. They worried that in its current form the backstop may leave the UK tied to the EU indefinitely.
In a statement earlier, the Commission said it had put forward proposals to try to reassure MPs the backstop "if used will apply temporarily".
A spokesman said the EU was willing to meet UK negotiators at any time.
He added: "We are committed to using our best endeavours to find a subsequent agreement that replaces the backstop... We are committed to ratifying this deal before 29 March."
Earlier, Mr Barnier said that talks about the UK's withdrawal from the bloc were now between the British government and MPs.