The Taoiseach has conceded that the UKs Withdrawal Agreement may now not be finalised until December or even January.
Hopes of an agreement on the Irish border issue were dashed this week after talks stalled last Sunday.
Yesterday, Leo Varadkar told EU leaders not to underestimate the risk of a return of violence in Northern Ireland.
During the EU Leaders Summit in Brussels, he held up a copy of the Irish Times reporting the story of a woman whose father was killed at a border post during the Troubles.
He said he wanted to use it as a prop to prove a point about violence in the North.
"That is what used to happen when we had Customs posts in Ireland," he said.
"I just wanted to make sure that there was no sense in the room that, in any way, anyone in Ireland or in the Irish Government was in any way exaggerating the real risk of a return to violence in Ireland."
The only tangible achievement to come out of summit this week was the possibility of an extension of the transition period after the UK leaves the bloc in March.
The transition period will see the UK effectively remaining in the EU Customs Union and Single Market for 21 months after it leaves, to allow time for a new trade deal to be agreed.
Yesterday, Mr Varadkar warned that a legally binding backstop preventing a hard border in Ireland would have to be finalised before any extension was agreed.
Meanwhile, the EUs chief Brexit negotiator Michel Barnier opened the door to the extension in the hope that Britain would agree to a “two-tier” backstop that would see the entire UK following EU rules during the transition – and Northern Ireland handed special status “unless and until” a new can be struck.
An extension would allow Mrs May to argue with skeptical MPs in Britain that the backstop will never come into play as there would be enough time available to secure a future trading deal preventing the need for it.
She has conceded that there a "few but considerable outstanding issues" in relation to the backstop.
She said she is committed to working with EU leaders to break the impasse adding, "there is a lot of hard work ahead; there will be more difficult moments as we enter the final stages of the talks.
"I am convinced that we will secure a good deal that is in the interests of the UK and the EU," she said.
The European Council President Donald Tusk noted that if the UK now felt an extension would be “helpful to reach a deal,” European leaders would be “ready to consider it positively.”
This evening, Leo Varadkar warned that businesses will 'bite back' if politicians can't finalise a Withdrawal Agreement by Christmas.
“Businesses are going to make plans long before that,” he said.
“The business sector operates on a quarter-by-quarter basis.
“Businesses, banks employers, airlines will start making decisions – and they will start making decisions that bite.”
The UK will leave the EU in March next year.
In order to ensure an orderly transition, a Withdrawal Agreement including a legally binding Irish border backstop will have to be finalised.
Without the backstop, the UK will crash out of the bloc without a deal.
Reporting from Sean Defoe in Brussels ...
