Update 3.44pm: Tánaiste Simon Coveney has today warned the UK there will be no Brexit withdrawal treaty if there is any U-Turn on the "backstop" solution to avoid a hard border on the island.
The Foreign Affairs Minister insisted that the UK government has provided a "cast-iron guarantee" that will ensure no physical infrastructure, checks, or controls at the border between Northern Ireland and the Republic, post-Brexit.
"Without that backstop agreement in place in the withdrawal treaty there will be no withdrawal treaty and there will be no transitional arrangements which are part of the withdrawal treaty," Mr Coveney warned.
The draft text of a Brexit treaty includes an agreement between the EU and the UK that there must be a backstop solution to ensure that there is no hard border on the island of Ireland.
Yesterday, the UK and EU agreed terms for a Brexit transition period.
Negotiators Michel Barnier and David Davis said the deal was a "decisive step" in the Brexit process.
Speaking during Leaders' Questions in the Dáil today, Mr Coveney hit back at claims that the Government had failed to make any progress on the Irish border issue.
Fianna Fáil TD Stephen Donnelly said he believed that what was agreed yesterday was a "political fudge".
He also said it was an attempt to "kick the (border issue) can down the road."
However, Mr Coveney said: "Now what we have is an agreement from the British negotiating team to put that backstop in the withdrawal agreement first so that we know there is a floor below which we cannot fall."
He added: "And they have also agreed, as a matter of urgency, they would engage in negotiation to put a legally operational backstop in place in the withdrawal agreement and that negotiation would start as soon as next week.
"I think you should inform yourself in terms of what is progress and what's not," he told Mr Donnelly.
Earlier: Taoiseach to meet Angela Merkel after UK agrees Brexit border 'backstop' deal
Taoiseach Leo Varadkar travels to Berlin to meet with German Chancellor Angela Merkel today.
Discussions will focus on the agenda for this week's meeting of the European Council, including Brexit.
They will be discussing their approach to the future of the European Union following yesterday's Brexit treaty deal.
A spokesperson for the Taoiseach says Britain's commitment to a Brexit border 'backstop' is legally firm and will apply until something better is agreed.
The 'transition' deal allows talks on the UK's future trade relationship with the EU to be triggered later this week.
Some issues remain undecided - including the border - but Tánaiste Simon Coveney says that does not mean it has been kicked into the long grass.
Labour Party leader Brendan Howlin has warned that we are no closer to coming up with a way to put the ‘backstop’ in place that would be agreeable to all sides.
- Digital Desk and PA