Taoiseach Leo Varadkar has been accused of disrespecting the people of Northern Ireland by a DUP MP.
Jim Shannon said power for Northern Ireland politics rested at Westminster – and "certainly doesn't lie" with the Taoiseach.
It came as former shadow Scottish secretary Ian Murray, a Labour MP, said the DUP were "holding this Government round the neck" as British prime minister Theresa May attempted to hold on to power.
Reports suggested that DUP leader Arlene Foster had voiced strong opposition to a proposal she claimed would see Northern Ireland treated differently from the rest of the UK, as part of Brexit negotiations over the Irish Border.
The British government’s majority in the Commons is dependent on its confidence-and-supply deal with the DUP at Westminster.
Strangford MP Mr Shannon told Mr Murray: "Will he also acknowledge the disrespect that the Taoiseach has shown to the people of Northern Ireland today, whenever he said that he now speaks for the people of Northern Ireland, and the DUP and other elected parties don't.
“Is it not time that he knows exactly that the power for Northern Ireland, for democracy, for the political process, is here in this chamber.
“And it certainly doesn’t lie with Leo Varadkar, as the Taoiseach of the Republic of Ireland.”
Mr Murray replied: "I think in the chamber, in the country or anybody who happens to be watching these proceedings will see that the three members of the Democratic Unionist Party that are sitting in this chamber are the real government in this House.
‘Dictating the terms’
"They are dictating the terms of Brexit. The member who's just intervened on me, the honourable gentleman, is no doubt the de facto secretary of state for exiting the European Union, in terms of the power they have over the prime minister.
“It’s clear, as I said earlier, that between courses at lunch this afternoon the prime minister has gone from a negotiated agreement to a set of texts, to throwing it in the bin alongside any leftovers from the lunch.
“It’s clear that the Democratic Unionist Party, 10 members of parliament from Northern Ireland, are holding this government to account, are holding this government round the neck, because it’s much more important for the prime minister to hold on to power than it is to do what’s in the best interest of all of our nations.”
Mr Murray had earlier said events in Brussels on Monday were a "farce" and that Ms Foster "controls the government" and was "the real de facto prime minister in this country".
He bemoaned the fact that journalists on Twitter appeared to have more information on Ms May’s meetings on Monday than other MPs.
DUP MP Ian Paisley (North Antrim) said: "I don't think anyone should get their news constantly from Twitter.
“But on the key point, on all of these clauses, should we not show discernment and skill and make sure that we don’t fall for the spin, whether it comes out of Dublin or London or Brussels?
“Let this negotiation run and let’s see what comes out of it at the end.”
Earlier there was swift political reaction to the failure on Monday to deliver a deal on Brexit between the UK and EU.
European Council president Donald Tusk made clear in a tweet that he had been preparing to move negotiations on to the second phase of negotiations until the last-minute call for more time.
“I was ready to present draft EU 27 guidelines tomorrow for Brexit talks on transition and future. But UK and Commission asked for more time,” said Mr Tusk.
“It is now getting very tight but agreement at December European Council is still possible.”
Regulatory alignment
A deal on regulatory alignment could mean both Ireland and Northern Ireland following the same rules governing trade, in order to ensure goods can continue to move freely across a “soft” Irish Border with no checks. But critics say that this solution would effectively move the customs border between the UK and the Republic into the Irish Sea.
Leaders of devolved governments in Scotland and Wales and even the mayor of London complicated matters by announcing that if Northern Ireland was to be offered any such special status after Brexit, other parts of the UK should be offered a similar opportunity.
Scottish first minister Nicola Sturgeon, who opposes Brexit, said: "If one part of UK can retain regulatory alignment with EU and effectively stay in the single market – which is the right solution for Northern Ireland – there is surely no good practical reason why others can't."
Welsh first minister Carwyn Jones said: “We cannot allow different parts of the UK to be more favourably treated than others.
“If one part of the UK is granted continued participation in the single market and customs union, then we fully expect to be made the same offer.”
‘Huge ramifications’
London's Labour mayor Sadiq Khan said the deal being discussed in Brussels would have "huge ramifications for London", which voted overwhelmingly to remain in the EU.
“If Theresa May has conceded that it’s possible for part of the UK to remain within the single market and customs union after Brexit ... and a similar deal here could protect tens of thousands of jobs,” said Mr Khan.
Conservative MPs and peers who were briefed in Westminster by Brexit minister Steve Baker and Ms May's chief of staff Gavin Barwell said they had been given the impression the PM had not agreed to Irish proposals on keeping Northern Irish regulations in line with the south.
Leading Brexiter Jacob Rees-Mogg told reporters: “I don’t think that can possibly happen. The government doesn’t have a majority for that.”
And backbench Remain supporter Anna Soubry said that the "simple solution" would be for the whole of the UK to remain in the single market and customs union.
‘Everybody is agreed’
“Nobody could want one part of our country to have a different set of rules to another part of our country,” said Ms Soubry. “On that, everybody is agreed.”
Mr Rees-Mogg said that Dublin was "promoting the creation of a united Ireland" by trying to force Britain's hand on the Border. But Taoiseach Leo Varadkar insisted there was "no hidden agenda" and that his policy was driven by the terms of the Belfast Agreement which sealed the peace process.
British Labour leader Jeremy Corbyn said: "The real reason for today's failure is the grubby deal the government did with the DUP after the election.
“Each passing day provides further evidence that Theresa May’s government is completely ill-equipped to negotiate a successful Brexit deal for our country.” – Press Association