Minister for Foreign Affairs Simon Coveney has said the British government has created a new "red line" barrier to progress that it knows the EU cannot move on.
In a post on Twitter, he said the European Union was working seriously to resolve practical issues with the implementation of the Northern Ireland Protocol.
"Real Q: Does UKG actually want an agreed way forward or a further breakdown in relations?" Mr Coveney tweeted.
With the EU due to put forward proposals in the coming week aimed at breaking the post-Brexit impasse over the protocol, the UK is set to call for "significant change" to the measure, which avoids a hard border on the island of Ireland.
After Mr Coveney's tweet was posted, the UK's Brexit Minister, David Frost, responded saying that he preferred "not to do negotiations by twitter".
He said the "issue of governance and the CJEU (European Court of Justice) is not new. We set out our concerns three months ago in our 12 July Command Paper.
"The problem is that too few people seem to have listened".
In a speech ahead of Wednesday's tabling of proposals by the EU, Mr Frost is to reiterate the UK's desire to strip the European Court of Justice of its role governing the protocol, which he will say has "created a deep imbalance".
European Commission Vice-President Maroš Šefčovič, who oversees post-Brexit relations with Britain, said on Thursday the EU's executive would finalise measures next week aimed at resolving post-Brexit trading issues in Northern Ireland by the end of the year or early 2022.
But Mr Šefčovič reiterated that he would not renegotiate the protocol, and that solutions would have to be found within the terms of a deal designed to keep an open border between Northern Ireland and the Republic.
Mr Frost is due to give a speech to the diplomatic community in the Portuguese capital, Lisbon, on Tuesday.
He is expected to say endless negotiation is not an option and that the UK government will need to act using the Article 16 safeguard mechanism if solutions cannot be agreed rapidly, according to extracts of his speech released by his office.
Article 16 allows either side to take unilateral action if the protocol is deemed to have a negative impact.
EU working seriously to resolve practical issues with implementation of Protocol - so UKG creates a new "red line" barrier to progress, that they know EU can't move on…. are we surprised?— Simon Coveney (@simoncoveney) October 9, 2021
Real Q: Does UKG actually want an agreed way forward or a further breakdown in relations? https://t.co/4MhgEdlxAf
1. I prefer not to do negotiations by twitter, but since @simoncoveney has begun the process...— David Frost (@DavidGHFrost) October 9, 2021
...the issue of governance & the CJEU is not new. We set out our concerns three months ago in our 21 July Command Paper.
The problem is that too few people seem to have listened. https://t.co/Y7DDdgu0pC
"No one should be in any doubt about the seriousness of the situation ... The EU now needs to show ambition and willingness to tackle the fundamental issues at the heart of the protocol head on," the speech transcript said.
"The UK-EU relationship is under strain, but it doesn't have to be this way. By putting the protocol on a durable footing, we have the opportunity to move past the difficulties of the past year."
Mr Frost is also expected to signal a desire to free the protocol from the oversight of European judges.
"The role of the European Court of Justice (ECJ) in Northern Ireland and the consequent inability of the UK government to implement the very sensitive arrangements in the protocol in a reasonable way has created a deep imbalance in the way the protocol operates," the transcript said.
"Without new arrangements in this area the protocol will never have the support it needs to survive."
In his post on Twitter, Mr Frost said the UK will await the proposals from Mr Sefcovic.
"We will look at them seriously & positively whatever they say. We will discuss them seriously and intensively. But there needs to be significant change to the current situation if there is to be a positive outcome."
2. We await proposals from @MarosSefcovic. We will look at them seriously & positively whatever they say. We will discuss them seriously and intensively.— David Frost (@DavidGHFrost) October 9, 2021
But there needs to be significant change to the current situation if there is to be a positive outcome.
Responding to the overnight exchange of tweets between Minister Coveney and Mr Frost, Stephen Kelly of Manufacturing NI, said it did not set a good tone for what would be an important week.
He said the UK, the EU and business had been working hard over the summer to find ways to simplify what happened in the Irish Sea.
"It set the week off in a more sour mood rather than a more positive and optimistic mood. Business in NI has been very clear, they'd like both sides to sit down, they'd like both sides to sit down with business. I think together we'd be able to work through the problems that are here.
"But I think starting the week off with a row, doesn't set the tone that's needed in a week where we need trust and we need responsibility being taken."
Mr Kelly said the issue of the jurisdiction of the European Court of Justice was not one that business in NI was raising.
"In the ten months since the UK and EU agreed the operational plan for the protocol, I've had nobody in business either directly, in meetings that we've had with both sides, or in visits that both sides have had with business, no-one raised the issue of the European Court of Justice.
"In fact it's critical in many respects in terms of NI's access to the Single Market for goods, so we would hope that while there's been a spat overnight online, we'd hope that when they get into the room ... they'll recognise that there's an opportunity here for NI and we need to grasp it."
Meanwhile, writing in the Telegraph, DUP leaderr Jeffrey Donaldson said in recent days a "route map for progress seems to be emerging".
But he said he wanted to see "concrete legislative changes" which dealt with the challenges presented by the protocol for agri-food, agrifood and supermarkets.
He said if Northern Ireland's place within the UK's internal market was not restored then the British government should take unilateral action to do it.
He said he wanted the "removal of the Irish Sea border and its impact on our trading and constitutional position".
Additional reporting Conor Macauley