The timetable for reaching a Brexit deal was thrown into doubt on Sunday night after talks failed to reach an agreement.
A hastily arranged meeting between Brexit Secretary Dominic Raab and European Union negotiator Michel Barnier could not produce a breakthrough, leaving the process on a knife-edge ahead of a key summit on Wednesday.
Mr Barnier said that “despite intense efforts” there had been a failure to reach agreement on one of the trickiest aspects of the negotiations - how to prevent a hard border with Ireland.
The Government said there were still “unresolved issues” relating to the Irish backstop but it remained committed to making progress at this week’s summit of EU leaders.
ITV News Political Editor Robert Peston said the reason for the failure to come to an agreement was because the EU wants a "backstop to the backstop" - which would keep just Northern Ireland in the customs union and single market, effectively creating a border between Northern Ireland the rest of the UK.
The surprise announcement of the meeting between Mr Raab and Mr Barnier fuelled rumours a deal was set to be done ahead of this week’s European Council meeting.
But after talks which lasted a little over an hour, it was clear that major obstacles remained.
- What went wrong in Brussels on Sunday? ITV News Correspondent Angus Walker explains:
The Prime Minister’s room for manoeuvre is severely restricted, with opposition to both the EU’s proposed backstop and concerns about her own alternative.
The EU version, which would see just Northern Ireland remain aligned with Brussels’ rules, has been called unacceptable by Mrs May and is loathed by the DUP.
Mrs May’s counter-proposal for a “temporary customs arrangement” for the whole UK is viewed suspiciously by Brexiteers who fear it becoming an indefinite position which would prevent free trade deals with countries around the world.
Agreeing to such a measure could trigger a Cabinet revolt and the potential resignation of senior ministers.
However, senior Cabinet minister Jeremy Hunt gave Mrs May his full backing on Monday saying that "everyone in the UK should have confidence that Theresa May will never sign a deal that is not compatible with the letter and spirit of the referendum result".
He continued that the Government "firmly believes that we can find a deal on that basis that works for the EU and our partners and friends in Europe", but that negotiations are currently in a "difficult period".
The Foreign Secretary added: "We should remember that a huge amount of progress has been made, but there are one or two very big outstanding issues.
"I think we can still get there, whether we do this week or not, who knows?"
Mr Hunt said everyone involved in the Brexit negotiations was "trying incredibly hard to get deal" and that "it's possible to do it with good will on all sides, but there are some difficult issues to overcome".
Likewise, International Development Secretary Penny Mordaunt gave her backing to Mrs May saying that "everyone is getting on with their jobs, we are supporting the PM to get the best deal for the country.
"Everybody needs to calm down, we are entering the final stage of these negotiations and we are all behind the PM trying to get the best result.”
Writing in his Daily Telegraph column, former foreign secretary Boris Johnson said the backstop idea as a whole should be jettisoned and called on Theresa May to "stand up to EU bullies".
"Like some chess player triumphantly forking our king and our queen, the EU Commission is offering the UK government what appears to be a binary choice," he said.
"It is a choice between the break-up of this country, or the subjugation of this country, between separation or submission.
"It must be rejected, and it must be rejected now. "
A special EU summit pencilled in for November to sign off a Brexit agreement could instead end up being used as an emergency meeting to discuss “no-deal” plans.
Talks will take place on Monday between DUP leader Arlene Foster and Taoiseach Leo Varadkar, while Mrs May will meet Sinn Fein leader Mary Lou McDonald in Westminster.