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.
Cabinet Office Minister David Lidington announced the changes to the Commons shortly before, saying they would mean the EU “cannot try to trap the UK in the [Irish] backstop indefinitely”.
Shadow Brexit secretary Keir Starmer questioned whether any changes had been made to the withdrawal agreement.
Replying to Mr Lidington’s statement in the Commons, he said: “People will be disappointed when they look at the detail.”
Theresa May flew out to the European Parliament late on Monday with her Brexit Secretary Steve Barclay for last-ditch talks ahead of MPs voting on her deal on Tuesday.
In the discussions with Mr Juncker and the EU’s chief Brexit negotiator Michel Barnier, two documents were agreed by all parties, which Mr Lidington said would “strengthen and improve” both the withdrawal agreement from the EU and the political declaration on the future relationship.
The first is a “joint legally-binding instrument” on the withdrawal agreement.
Mrs May said it could be used to start a “formal dispute” against the EU if it tried to keep the UK tied into the backstop – the safety net designed to maintain an open border on the island of Ireland – indefinitely.
The second is a “joint statement” adding to the political declaration to commit to replacing the backstop with alternative arrangements by December 2020.
Mrs May said: “MPs were clear that legal changes were needed to the backstop. Today we have secured legal changes.
“Now is the time to come together to back this improved Brexit deal and deliver on the instruction of the British people.”