There has been a broad welcome for the Brexit deal agreed this morning from across the Irish political spectrum, accompanied by an acceptance that challenges lie ahead.

Taoiseach Leo Varadkar said the deal had "achieved all we set out to achieve", adding: "This is not the end, it is the end of the beginning."

Flanked by Minister of State for European Affairs Helen McEntee and Minister for Foreign Affairs Simon Coveney, the Taoiseach said "we want to build bridges and not borders" and want the provisions of the Good Friday Agreement to continue after Brexit.

Mr Varadkar said: "I am satisfied that sufficient progress has now been made on Irish issues, the parameters have now been set and they are good."

He said Ireland's focus would now move to Phase 2 of the negotiations.

Mr Varadkar said he wanted to assure unionists of his motivations.

"There is no question of us trying to exploit Brexit to move toward Irish unity without consent," he said.

He also told the "Nationalist people of Northern Ireland" that their birthright as Irish citizens will not be affected by the Brexit deal.

Mr Varadkar said the Common Travel Area will continue and British and Irish citizens can live and work freely in each other's countries.

The avoidance of a hard border as an "overarching requirement" of any future decisions will be guaranteed.

The Taoiseach said his preferred option is "a deep and comprehensive agreement" between EU and UK to allow trade as we do now.

If this is not possible, a backstop arrangement will allow full alignment between north and south going forward.

Secretary of State for Northern Ireland James Brokenshire said he was "delighted" the Commission had made "sufficient progress" .

In a statement this afternoon, Mr Brokenshire said: "We will protect Northern Ireland's integral place in the internal market of the UK with full, unfettered access for Northern Ireland's businesses. 

He added: "We will avoid a hard border between Northern Ireland and Ireland and protect the Belfast Agreement. We remain determined to negotiate a Brexit that works for everyone, in all parts of the United Kingdom."

Earlier, the Tánaiste described the deal reached in the Brexit talks this morning as positive.

Speaking on RTÉ’s Morning Ireland, Simon Coveney said it was good news for anyone, whether you are nationalist or unionist, and living on border communities.

He said that they know now what the default position is and in absence of agreed solutions in Phase 2 there is a "fallback position".

Mr Coveney said that "what is being said is there is commitment in the absence of agreed solutions - in other words if there is no deal on a bigger deal that solves all these issues, well then there is commitment to maintain full alignment with the rules of the internal market and customs union.

"In other words that would be an arrangement accepted by the UK and the EU in this wording that will prevent any need for border checks, which is exactly what we are looking for.

"The default position is that the island of Ireland will maintain full alignment with Northern Ireland. There will be in no circumstances a need to introduce border checks on the border of Ireland."

Mr Coveney said the language that has changed between the deal that was almost agreed on Monday is an extra paragraph which gives reassurances to businesses.

"We have no issue with that paragraph at all. It is saying that while there is full protection for full trade on the island of Ireland, the British government is also saying they will ensure there are no barriers to trade between Northern Ireland and the rest of the United Kingdom."

He said this deal is not just about the DUP, though they have made a strong case this week.

He said the Irish Government could not have moved on to Phase 2 without an assurance of no hard border.

"We have always accepted is that the British government wants to negotiate a very comprehensive trade deal in Phase 2 and that may be possible.

"What we have always asked is the reassurance if that new deal doesn't deal with specific important Irish issues, we need and assurance that Ireland is protected," he said.

Sinn Féin's Mary Lou McDonald has said some of the language contained in the deal is to welcomed as it recognises the "unique and special circumstances of Ireland."

Also speaking on Morning Ireland she said it also recognises the sensitivities and the importance of the architecture around the Good Friday Agreement.

However, she added that care is needed "in the midst of considerable hype" not to miss a number of points, including Mrs May's repeated insistence that Northern Ireland will leave the single market and customs union.

Ms McDonald added that this presents a real and present danger.

Party leader leader Gerry Adams has said there are some positive elements in the Brexit documents, but he also expressed concern that issues relating to the European Court of Justice will not be dealt with until the next phase.

Fianna Fáil leader Micheál Martin, has welcomed the advances that have been made to progress into phase 2 of negotiations, and the North-South commitment that has been given.

Speaking on RTÉ’s Today with Sean O'Rourke, he said some key issues will have to be resolved in Phase 2.

He said there is a "certain logic" that Britain is moving towards a softer Brexit, realising it is all round better for everyone concerned.

"I think from the British perspective, it seems to me, we are edging towards a softer Brexit, though that is not what some hardline Brexiteers want to hear," he said.

"There are certain realities dawning, that ultimately hopefully that is where we are heading. Because that is in the best interests of Irish jobs, businesses and the Irish economy."

He said there is a sense also that Northern Ireland now gets the best of both worlds.

Commissioner says Irish side made no concessions

The European Agriculture Commissioner has said the Irish side in the Brexit negotiations "made no concessions" in order to reach the agreement announced today, because it had the full support of the other 26 EU member states.

Speaking to RTÉ's Europe Editor Tony Connelly, Phil Hogan said this "significant agreement" would not have been possible if Ireland did not have the full backing of the other member states.

Commissioner Hogan said the discussion of the Irish issue as a separate strand in Phase 2 of the Brexit talks puts a "double lock on the agreement announced today."

He said if an outcome does not arise that deals with issues of concern to Ireland, "then there is a backstop", which he said is important to reassure cross-border traders.

The Commissioner said he believes there are some members of the British government who did not fully understand the implication of Brexit and "how difficult it is to negotiate a free trade agreement as a third country outside the EU."