Irish Prime Minister Leo Varadkar said he was "surprised and disappointed" on Monday (Dec 4) after Britain appeared to pull back from a predicted deal with European Union leaders on the status of the Irish border after Brexit.
A meeting on this with all political party leaders is set for lunchtime today.
Regulatory alignment could mean both Ireland and Northern Ireland following the same rules governing trade, to ensure that goods can continue to move freely across a "soft" border with no checks.
"Crucially it is clear that we want to move forward together, but on a couple of issues, differences do remain, which require further negotiation and consultation", said May before heading to meet President of the European Council Donald Tusk nearly one-hour late than scheduled.
The EU has had "enough time now to decide whether or not they are going to discuss trade with us, they need to get on with it and if they don't get on with it, the closer we get to walking away with no deal", she said.
Diplomats have been negotiating relentlessly over the past days to meet an EU imposed deadline of yesterday and the European Parliament's chief Brexit official said it was "50/50 to have something".
European Commission President Jean-Claude Juncker spoke to Irish Prime Minister Leo Varadkar by phone.
The Prime Minister was within touching distance on Monday of a reaching an agreement with the EU's Brexit taskforce on the so-called "divorce issues" after a frantic day of negotiations in Brussels.
"I am surprised and disappointed that the British government now appears not to be in a position to conclude what was agreed earlier today", Varadkar said at a press conference in Dublin.
The EU wants progress to be made before a summit later this month - only then will they agree for trade talks on Brexit to move forward.
The EU has demanded "sufficient progress" on key withdrawal issues - the UK's exit payment, citizens' rights and Irish border - before the second phase can start. The pro-British Unionist party opposes any special status that could take Northern Ireland further from Britain and closer to the Republic of Ireland. A British spokesman said: "With plenty of discussions still to go, Monday will be an important staging post on the road to the crucial December Council".