Ireland's Prime Minister Leo Varadkar said he was "surprised and disappointed" that an anticipated deal on Brexit was not reached on Monday.
He said Ireland could not go into a second phase of Brexit talks without "firm guarantees that there will not be a hard border in Ireland".
Mr Varadkar said the UK had agreed a text that met Irish concerns.
However, he was then later told that the British government was not in a position to conclude "what was agreed".
The taoiseach told a press conference in Dublin that earlier on Monday, he had been in touch with EU Commission President Jean-Claude Juncker and EU Council President Donald Tusk and confirmed to both Ireland's agreement on the form of words about the Irish border.
But the deal did not go ahead.
The BBC's Laura Kuenssberg said the deal broke down after the DUP refused to accept UK concessions on the Irish border issue.
Prime Minister Theresa May is understood to have broken off from talks with Mr Junker to speak to DUP leader Arlene Foster.
It happened after the DUP leader had held a press conference saying her party would "not accept any form of regulatory divergence" that separates Northern Ireland from the rest of the UK.
However, Downing Street sources insist it was not only the intervention by the DUP that meant a deal was not concluded.
It is understood that there are still differences of opinion over citizens' rights, the role of the European Courts after the implementation period and also over the technicalities of the Irish border.
The UK was reportedly prepared to accept that Northern Ireland may remain in the EU's customs union and single market in all but name.
At her press conference on Monday afternoon, Mrs Foster accused Dublin of trying to change the 1998 Belfast Agreement without unionists' consent.
"We will not stand for that," she said.
"The prime minister has told the House of Commons that there will be no border in the Irish Sea and the prime minister has been clear that the UK is leaving the EU as a whole and that the territorial and economic integrity of the UK will be protected," said the DUP leader.
The Irish prime minister told a news conference that it "would not be helpful" for him to attribute blame for the breakdown in agreement.
When asked about the DUP's influence with the UK government, Mr Varadkar said that although they are the largest party in Northern Ireland, and their views have to be taken into account, they "don't represent the majority of people in Northern Ireland".
He added that the majority of people in Northern Ireland voted to remain in the EU during the Brexit referendum.
The Irish government had been seeking guarantees from the UK that there would be no customs checks on the border with Northern Ireland after Brexit and movements of goods and people would remain seamless.
John O'Dowd, Sinn Féin, accused the DUP leader, Mrs Foster, of putting party political needs ahead of border issues.
"It appears from the leaks of the paper that were presented today – and we will examine the paper in its totality – that there is certainly a significant section of the UK government who are prepared to treat us different because they either understand the unique circumstances of this island or they accept that these talks are going nowhere until this matter is dealt with," he said.
UK Prime Minister Theresa May has been meeting key EU figures in an attempt to hammer out a deal ahead of a summit in 10 days time.
Mr Tusk represents the leaders of the other 27 EU members, who all need to agree for there to be a move to the next phase of talks.
The UK voted for Brexit last year and is due to leave in March 2019, but negotiations have been deadlocked over three so-called separation issues: the status of expat citizens, the "divorce" bill and the Northern Ireland border.
The Good Friday Agreement or Belfast Agreement was reached on 10 April 1998 by the British and Irish governments and most of the political parties in Northern Ireland about how NI should be governed.
The agreement aimed to set up a nationalist and unionist power-sharing government in Northern Ireland.