European Commission president Jean-Claude Juncker has warned the UK there will be no Brexit deal without agreement on the Irish border.
On a visit to Dublin, Mr Juncker said fellow EU member states would not let Ireland be "isolated" on the impasse, insisting the demand for a resolution was a Europe-wide demand.
Amid an ongoing stand-off over how to maintain a free-flowing border post-Brexit, Mr Juncker assured Taoiseach Leo Varadkar that the EU would not waver on what he made clear was a pivotal issue.
Mr Juncker arrived in Dublin on Thursday morning for a two-day visit as the impasse between the EU and the UK over the border continues.
Coming a week ahead of a crunch European Council meeting of leaders in Brussels, the visit is a clear demonstration of the EU's solidarity with the Republic's position.
After a meeting with Mr Varadkar in Government Buildings, Mr Juncker made clear that a resolution to the border issue was crucial to the withdrawal treaty.
"This is not a bilateral question between Ireland the United Kingdom - this is an issue between the UK and the European Union," he said.
"We want to make it clear again and again that Ireland is not alone.
"We have Ireland backed by 26 member states and the Commission - this will not change.
"I am strongly against any temptation to isolate Ireland and not to conclude the deal on Ireland.
"Ireland has to be part of the deal."
Mr Varadkar said there was an urgent need to "intensify" negotiations to find an agreement on the shape of the border backstop.
"A withdrawal agreement without a backstop is of no use whatsoever," he said.
He added: "Let me blunt, there isn't much time left if we are to conclude an agreement and have it operational by the time the United Kingdom leaves the European Union next March."
Asked about wrangling within the UK government over the customs issue, the taoiseach said: "Internal British politics isn't my concern. My job is to represent my country, Ireland, and to do that as part of the European Union and we remain at the heart of the European Union.
"The most important aspect of the withdrawal agreement for us is the backstop, and British prime minister May committed in March that there would be a backstop and outlined in December what that backstop would contain."
This week the EU warned that more work was needed on how to deal with the 300-mile border, the UK's only land frontier with a European state, and protect frictionless movement after the withdrawal.
Mr Juncker started his visit with a meeting with Mr Varadkar and Mr Coveney at Government Buildings. He will later receive an honorary doctorate from the National University of Ireland and attend an official dinner hosted by Mr Varadkar in Dublin Castle.
Mr Juncker also addressed the Oireachtas this morning. He began by joking he would prefer to be drunk.
He then spoke of his fondness for Ireland, saying over the years he has spent some emotional times in Dublin, recalling in particular the summit in 1996 over the single currency.
Mr Juncker restated his commitment to the Republic as the deadline to Brexit approaches.
"Sometimes at the European Parliament, some of the members there are saying that this is not our business but that this is a bilateral business between Ireland and the UK - we do not share that view."
There was applause in the Oireachtas when Mr Juncker restated his commitment to the Republic.
"Ireland will come first... there are those that think the other 26 countries will abandon Ireland for a deal that suits them.
"Ireland's border is Europe's border and it is our priority."
Referring to the UK's imminent departure from the EU, Mr Juncker told the Oireachtas that there is no deal as good as membership of the EU.
"It simply does not exist," he said, adding that the prospect of the UK leaving the EU without any deal at all must be prepared for."
Taoiseach Leo Varadkar paid tribute to Europe for "transforming Ireland".
"For us, Europe enabled our transformation from being a country on the periphery of the continent, to an island at the centre of the world, at the heart of the common European home that we helped to build," Mr Varadkar said.
"The greatest challenge we face on this island is to unwrap the enigma, and solve the riddle of Brexit.
"It's as tricky as it sounds, so we are grateful for the diligence and understanding shown by the Commission's lead negotiator, Michel Barnier, in his conduct of these very difficult negotiations for the EU."
Speaking to the Oireachtas, the taoiseach thanked Mr Juncker for his words of support.
"We are so deeply grateful for the remarkable solidarity and support we have received from the EU institutions and fellow member states, none more so than from President Juncker," Mr Varadkar said.
"There has been consistent recognition of the unique position of Northern Ireland, and the unique situation in which it has been put by the decision of the UK to leave the EU.
"There is no stronger evidence of how small countries benefit so much from EU membership and how membership matters."
Mr Varadkar added: "The moral and political compass of President Juncker has helped to provide direction for Europe, creating more opportunities for our citizens and a better future for all."
On Friday, Mr Juncker will meet President Michael D Higgins and visit Croke Park, and the GAA museum.
He will also watch a demonstration of Gaelic football and hurling.
Rules governing the border post-Brexit represent one of the most vexed issues facing the negotiators in Brussels.
Advances have been made in a number of areas, such as customs, VAT and nuclear waste regulation, EU chief negotiator Michel Barnier has said, but "a lot more work" needs to be done to meet the October deadline.
Mr Juncker will be accompanied on his engagement in Dublin on Thursday morning by Mr Barnier and EU agriculture commissioner Phil Hogan.
Mr Varadkar has suggested other countries will baulk at signing trade deals with the UK post-Brexit if British prime minister Theresa May fails to honour commitments made to the EU on the border issue.
Both sides have agreed to include a so-called "backstop" option in the withdrawal treaty, which would commit the UK to align with an EU regulatory framework in the absence of a wider trade deal.
But the shape of that fall-back remains a sticking point, with the EU rejecting a UK contention that it should only be temporary, even if a broader agreement fails to materialise.
On Wednesday, the European Parliament's chief Brexit co-ordinator told MPs the UK plan for a temporary customs backstop was "not acceptable" and any fall-back option cannot be time-limited.
Guy Verhofstadt said the Government's position that the backstop of continuing UK alignment with the EU customs union would cease by the end of 2021 if no other solution was found left him "puzzled".
Ahead of Mr Juncker's arrival in Dublin, the taoiseach said: "This is an important opportunity to assess the state of play in the Brexit negotiations.
"We need to see much more progress from the UK to implement the commitments they made in December and March, and I expect the UK's efforts to intensify in the period ahead."
He added: "President Juncker and I are both very committed to the European project and the benefits that it brings to citizens across the Union.
"We will also discuss other key items on the agenda of next week's meeting of the European Council such as trade, ensuring a stable euro, and equipping the Union with a budget for its future needs."
