Theresa May will travel to Dublin following a cabinet on Wednesday afternoon for talks on Brexit with Taioseach Leo Varadkar.
She will fly to Brussels later that evening ahead of the European Council meeting on Thursday, but no further meetings in the Belgian capital have yet been announced.
The British prime minister embarked on a whirlwind tour of European capitals on Tuesday to seek reassurances to get her deal through parliament, after cancelling a vote scheduled for Tuesday which she accepted she would lose heavily.
Downing Street said Mrs May would bring her Brexit deal back before the House of Commons "before January 21".
- Sir John Major warns of return to worst days of Troubles
- Labour MP Conor McGinn: Jeremy Corbyn risks party's reputation as 'protectors of the Good Friday Agreement'
- Brian Feeney: Customs union and single market are real issues, not Brexit backstop
However, she was dealt a blow as European Commission president Jean-Claude Juncker declared there was "no room whatsoever for renegotiation" of the Withdrawal Agreement reached last month.
Sammy Wilson said Mrs May went to Europe yesterday with a mindset that would "guarantee she comes back with nothing which is going to alleviate the fears" of the DUP.
The DUP MP said she could only come back from talks with reassurances over the Irish border backstop which "don't mean anything when they are put against a legally-binding international agreement".
He said that holding and losing a meaningful vote would have strengthened Mrs May's bargaining position and urged her to call the EU's bluff by forcing it to choose between a no-deal Brexit or greater flexibility.
"The pressure is on the EU because don't forget the European Union say they don't want no-deal either," he said.
- Theresa May brushes aside speculation of impending vote of no confidence
- Leo Varadkar says Britain could avoid no deal Brexit by revoking Article 50
"The EU want our money and there is £39 billion resting on it.
"Do they really want to have to run around the capitals of Europe trying to fill up the hole in the budget which a no-deal situation would result in?
"Secondly, they need to have access to our market. Don't forget the EU countries have a 92 billion trade surplus with us so they cannot afford the impact which it may have on their jobs, on their factories, on their industry and their economies.
"We are always told the pressure is on Britain, [but] the pressure is on the EU unless we buckle."
Mr Juncker told MEPs the agreement was the "best deal possible" and the "only deal possible". But he offered a glimmer of hope to Mrs May by saying there was room to give "further clarifications and further interpretations without opening the Withdrawal Agreement".
The delay to the so-called "meaningful vote" by MPs means that ratification may not be possible until as late as 10 weeks before the scheduled date of Brexit on March 29. But Mrs May's spokesman insisted she continues to believe that necessary preparations can be completed within that time.
The Prime Minister held talks over breakfast with her Dutch counterpart, Mark Rutte in The Hague, which Downing Street described as "constructive".
Mrs May told the Dutch PM that "additional assurances" would be needed on the backstop arrangement to keep the Irish border open after Brexit if the deal was to get through parliament.
Mrs May then flew on to Berlin for a meeting with German chancellor Angela Merkel before going to Brussels for talks with Mr Juncker and European Council president Donald Tusk.
Mr Juncker won applause from MEPs as he said: "There is no room whatsoever for renegotiation, but of course there is room if used intelligently, there is room enough to give further clarifications and further interpretations without opening the Withdrawal Agreement.
"This will not happen. Everyone has to note that the Withdrawal Agreement will not be reopened.
"The deal we have achieved is the best deal possible - it is the only deal possible."