The Taoiseach Leo Varadkar has said Ireland has got a "satisfactory outcome" for its priorities in Brexit.
He was speaking after British Prime Minister Theresa May said her cabinet has agreed to support a draft deal.
She made the statement outside Downing Street in London, following a mammoth cabinet meeting.
In a statement earlier, Mrs May said: "The cabinet has just had a long, detailed and impassioned debate on the draft withdrawal agreement and the outlying political declaration on our future relationship with the European Union.
"These documents were the result of thousands of hours of hard negotiation by UK officials and many, many meetings which I and other ministers held with our EU counterparts.
"I firmly believe that the draft withdrawal agreement was the best that could be negotiated and it was for the cabinet to decide whether to move on in the talks.
"The choices before us were difficult, particularly in relation to the Northern Ireland backstop.
British Prime Minister Theresa May makes a statement outside 10 Downing Street, London | Image: Victoria Jones/PA Wire/PA Images
"But the collective decision of cabinet was that the government should agree the draft withdrawal agreement and the outlying political declaration.
"This is a decisive step which enables us to move on and finalise the deal in the days ahead".
"These decisions were not taken likely, but I believe it is a decision that is firmly in the national interest.
"When you strip away the detail, the choice before us is clear: this deal which delivers on the vote of the referendum, which brings back control of our money, laws and borders, ends free movement, protects jobs, security and our union - or leave with no deal or no Brexit at all.
"I know that there will be difficult days ahead - this is a decision which will come under intense scrutiny, and that is entirely as it should be".
Taoiseach Leo Varadkar speaks at a press conference on Brexit at Government Buildings in Dublin | Image: Niall Carson/PA Wire/PA Images
In response to the developments, Mr Varadkar said: "While I welcome these developments let me say at the outset: that Brexit is not our policy and is something that we regret.
"However we respect the vote of the United Kingdom's people and their decision to leave".
"Once the outcome of the UK referendum was known, we identified our national priorities.
"These were, and are, protecting the peace process and the Good Friday Agreement, maintaining the Common travel Area and related benefits for Irish and British citizens, re-affirming our place at the heart of the European Union and protecting trade, jobs and the economy.
"On each of these priorities, we have reached a satisfactory outcome today".
I am pleased an agreement has been reached between EU & UK negotiators on a draft #Brexit Withdrawal Treaty. While I welcome these developments, Brexit is not our policy & is something we regret. However we respect the vote of the people of the UK. pic.twitter.com/ff4HLr2XAs
— Leo Varadkar (@campaignforleo) November 14, 2018
"Avoiding a hard border has been one of the most difficult challenges - the December report envisaged that the best way to avoid a hard borer was to agree a comprehensive future relationship that would render a border unnecessary.
"This is still our shared objective and preferred outcome.
"But we've always said that we'd also need what has become known as the backstop.
"This now fully spelt out in the draft withdrawal agreement."
"The text makes clear that this backstop would apply 'unless and until' a better solution is agreed.
"I firmly hope that we can achieve a better solution, and we will be working strenuously to that end - but we do now have the insurance policy of the backstop to apply if all other efforts fail to produce a better solution".
He also paid tribute to Mrs May for "honouring her promise to protect the peace process and the Good Friday Agreement."
European Union chief Brexit negotiator Michel Barnier at the European Council in Brussels | Image: Zheng Huansong/Xinhua News Agency/PA Images
Backstop 'not meant to be used'
The EU chief Brexit negotiator Michel Barnier said the draft deal is "a decisive, crucial step" in concluding the negotiations.
"We have now found a solution together, with the UK, to avoid a hard border on the island of Ireland.
"First we will use our best endeavours to solve this issue for the long-term through a future agreement.
"If we are not ready by July 2020, we could jointly consider extending the transition to provide for more time.
"Only if, at the end if the transition - extended or not - we are still not there with a future agreement would the backstop solution that we agreed today kick-in.
"This backstop solution has evolved considerably from the original EU proposal from February this year".
"in the backstop scenario, we agreed to create an EU-UK single customs territory - Northern Ireland will therefore remain in this same custom territory as the rest of the UK.
"In addition, Northern Ireland would remain aligned to those rules of the single market that are essential for avoiding a hard border".
He added: "This backstop is not meant to be used - our objective remains to reach the new agreement between the EU and the UK before the end of the transition".
The European Commission has published the full draft agreement, which stretches to 585 pages.
On the issue of the backstop agreement, it said there will be "full alignment" "unless and until" a new deal is reached.
This clause is also not time-limited.
It also commits to avoiding a hard Irish border "including any physical infrastructure or related checks and controls".
Backstop is maintaining "full alignment" and is "unless and until" a new deal. Not time limited. Also commitment to avoiding a hard border "including any physical infrastructure or related checks and
controls" #Brexit pic.twitter.com/MwMIFD1j2Z— Sean Defoe (@SeanDefoe) November 14, 2018
