Theresa May has said she is “determined” to deliver Brexit on time, ahead of talks on the Irish backstop.
Writing in the Sunday Telegraph, the prime minister said she would return to Brussels with a “fresh mandate, new ideas and a renewed determination”.
MPs have voted to seek an “alternative arrangement” to guarantee the Northern Ireland border stays open after Brexit.
But the Irish deputy prime minister has said “there are no credible alternative arrangements” to the proposal.
Writing in the Sunday Times, Simon Coveney said: “The EU will not renegotiate the withdrawal agreement and there will be no withdrawal agreement without the backstop.”
Mr Coveney said the backstop was required to “ensure the protection of the Good Friday Agreement” which ended 30 years of armed struggle in Northern Ireland.
The backstop forms part of the withdrawal agreement negotiated by the UK and EU and is aimed at keeping the border between Northern Ireland and the Irish Republic open after Brexit.
The UK is due to leave the EU at 11:00 GMT on Friday 29 March, when the two-year time limit on withdrawal negotiations enforced by the Article 50 process expires.
Some MPs have suggested Britain will need more time to negotiate its exit to avoid crashing out of the EU without a deal.
Foreign Secretary Jeremy Hunt conceded on Thursday that “extra time” might be needed to get “critical legislation” related to Brexit through Parliament.
But Mrs May has insisted the departure date will not change, writing in the Telegraph that she would “deliver Brexit on time”.
Mrs May said she rejected the suggestion “that seeking alternative arrangements for the backstop constituted ‘ripping up the Good Friday Agreement'”.
The prime minister added that MPs wanted the government to go back to Brussels to renegotiate the deal after the Commons voted in favour of Tory backbencher Sir Graham Brady’s amendment on Tuesday that called for “alternative arrangements” to be found.