The DUP say they never assented to any of the wording which leaked out of the Brexit discussions, whether it be "no regulatory divergence" across the island of Ireland after Brexit or "continued regulatory alignment".
Theresa May and Jean-Claude Juncker were forced to admit it was not possible to strike a Brexit deal on Monday after a frantic day of negotiations came to a halt because Northern Ireland's DUP had not yet been signed up.
Extending EU's deadline by pledging to resume their talks later this week, he added.
However, the United Kingdom has rejected the deadline with a government spokesperson saying: "With plenty of discussions still to go, Monday will be an important staging post on the road to the crucial December Council". And a lot of progress has been made.
Border agreements are still being decided in the move towards Brexit.
According to the Irish Times this morning, Ireland and the United Kingdom have agreed a deal to ensure there will be no "Hard Border" between the Republic and Northern Ireland.
It would mean Northern Ireland businesses adhering to the same standards and rules as their southern counterparts.
One solution is to allow Northern Ireland to stay in the customs union when the rest of the United Kingdom leaves.More news: Polls: Moore in Slight Lead in Alabama Senate Race
More news: Mueller removed top Federal Bureau of Investigation agent over possible anti-Trump texts
More news: Micromax's Bharat 5 Stands No Chance Against The Redmi 5A
"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 Irish government remains hopeful, but at this stage it is very hard to make a prediction", the official added.
The failure to seal a deal threatens to delay the progression of the Brexit negotiations to the second phase covering trade and the UK's future relationship with the European Union (EU).
The issue of citizens' rights has also remained a hurdle. The lives of millions of families are at stake. "Getting closer to sufficient progress at December #EUCO".
Perhaps if the parliamentary arithmetic had been different, the prime minister might have pushed ahead and signed a deal with the European Union against the DUP's wishes.
While for months a divorce settlement on financial issues between the United Kingdom and the European Union represented the biggest hurdle to progress in talks, the United Kingdom last week mostly agreed to pay what the European Union has been asking for.
The UK government has repeatedly insisted many of these questions can not be answered until the next stage of Brexit talks - on a transition period and a future EU-UK trading and customs relationship - is allowed to begin.