Theresa May has been told during talks in Brussels the EU will not reopen the Brexit deal.
The prime minister told European Commission president Jean-Claude Juncker this morning British MPs wanted “legally binding” changes to the backstop.
But Juncker rebuffed the demand and said the EU would “not reopen the withdrawal agreement”.
The top EU official did declare “openness to add wording to the political declaration” – the basis of the future trading relationship between the EU and the UK – to be “more ambitious”.
May will meet Juncker again before the end of February “to take stock” of talks.
Brexit Secretary Stephen Barclay and EU chief negotiator Michel Barnier will meet next Monday.
May returned to Brussels for talks after MPs rejected her initial deal and voted in favour of a plan that would include “alternative arrangements” to the Northern Ireland backstop.
The backstop is the fallback position that would see the UK remain closely tied to EU rules if a full trade deal can not be agreed, and prevent a hard border in Ireland.
The UK is set to leave the EU in 50 days’ time, on March 29.
Today’s talks came after European Council president Donald Tusk angered some Tory Brexiteers by declaring there was a “special place in hell” for those who pushed for the UK to leave the EU without a plan.
Labour leader Jeremy Corbyn has told May he will support her deal if she meets a list of five demands.
The move has angered some pro-EU Labour MPs who want a second referendum to give voters the chance to vote for continued membership.
Owen Smith, a former leadership candidate, said today he was considering quitting the party.