Taoiseach Micheál Martin has said the DUP's threat to bring down the Northern Ireland institutions if changes to the Northern Ireland Protocol are not delivered has "created new challenges".
Mr Martin said the European Union is in solution mode, and wants to operate within the agreed arrangements to make the Northern Ireland Protocol work.
DUP leader Jeffrey Donaldson earlier announced his party's immediate withdrawal from cross-border political institutions established on the island of Ireland under the Good Friday Agreement.
Speaking in Co Cavan, Mr Martin said he was fully committed to maintaining the Good Friday Agreement.
"It's no secret that I'm passionately committed to maintaining the institutions of the Good Friday Agreement and their full operation in all aspects, north, south, the Executive and the Assembly and the British Irish dimension, so that's something I'm very committed to."
The Taoiseach met the European Commission vice-president Maroš Šefcovic ahead of his visit to Northern Ireland.
Mr Martin said they had a "very good comprehensive discussion" yesterday evening.
"In terms of the meeting I had with vice-president Sefcovic last evening and meetings I had on the weekend, with the UK side, I am clear that Europe is in solution mode, and that Europe wants to work hard within the existing arrangements to make the protocol work for the people of Northern Ireland," Mr Martin said.
"I hope that vice president Šefcovic went up today to listen and engage. From our perspective, we have listened to party views and met with all the other parties on this issue.
"What is clear is I think all parties would like to see a streamlining and more flexible operation of the protocol. The UK Government is saying to me that they want to get a solution."
Mr Donaldson issued the warning on the future of Stormont in a keynote address in Belfast on the same day as vice-president Šefcovic began a two-day visit to Northern Ireland.
Ahead of any move to pull ministers out of the coalition administration, a step that would bring down the power-sharing institutions, Mr Donaldson said his party was first seeking to challenge the legality of checks on goods arriving in Northern Ireland from Britain introduced under the protocol, and establish whether their implementation requires the approval of the Stormont Executive.
Speaking on RTÉ's Prime Time programme tonight, Mr Donaldson said he wanted to see progress made by mid-to-late October on issues surrounding the Northern Ireland Protocol, before his party potentially withdraws from the Stormont Executive.
He would not be drawn on an exact deadline or date, instead insisting on his wish for an assembly election to give his position on the protocol a mandate.
Pressed on the issue however, Mr Donaldson said: "We have made it clear that we need to see progress probably by mid to late October. There are good reasons for that."
"I simply am saying that I cannot sustain my position in government in circumstances where we have to preside over the imposition of a protocol that is harming Northern Ireland," he added.
Mr Donaldson disagreed that the party were seeking to collapse the Executive, saying: "I’m just doing what often happens with coalition governments, saying we cannot continue in circumstances where as unionists we’re expected to be involved in a protocol that is harming our relationship with the rest of the UK.
"That is not a tenable position for me as a unionist," he added. "Every day our economy is being harmed and undermined by this protocol"
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Sinn Féin leader Mary Lou McDonald today described the position as set out by Mr Donaldson as "reckless, irresponsible and [a] short-sighted election stunt".
"They are threatening the stability of the political institutions when we are in the midst of the Covid pandemic, when the Tories are putting families and workers under pressure with more cuts, and when there is big work to do on the issues that matter to people's everyday lives - on hospital waiting lists, on schools, on housing and on jobs, and on rebuilding our economy," she said.
Minister for Foreign Affairs Simon Coveney said that "no positive agenda" is served by breaking down the institutions of the Good Friday Agreement.
"We take unionist concerns in relation to the protocol seriously and we have consistently sought to listen and engage with those concerns, just as we have with the perspectives of everyone across Northern Ireland.
"The Taoiseach and Tánaiste met with Jeffrey Donaldson to discuss these issues in detail in the last two weeks.
"However, no positive agenda is served by blocking practical north/south co-operation or by the breakdown of the other institutions of the Good Friday Agreement," he said.
Reacting to Mr Donaldson's speech, Downing Street said the threat to collapse Stormont over the protocol showed the "real pressures" the agreement is causing.
Prime Minister Boris Johnson's official spokesperson said: "I think this illustrates the real pressures that the protocol is causing in Northern Ireland and the lack of cross-community support for the current arrangements.
"Without this support, the protocol cannot be sustainable for the long term. That's why we've published a command paper setting out the significant changes needed to put the protocol on durable footing, and we're engaging with talks with the EU to determine whether a constructive process can be established that addresses these issues."
He added: "We believe that the challenges the DUP and others have set out illustrates that the protocol in its current form is simply not sustainable."
SDLP leader Colum Eastwood has said Mr Donaldson's comments are "dangerous" and said he is not learning the lessons of history.
Speaking on RTÉ's News at One, he said by threatening to bring down the institutions and walking away from a key part of the Good Friday Agreement "which is the North/South institutions", is extremely naive and dangerous.
"The outworkings of what Jeffrey really wants, if his logic was brought to the end point, you are looking at a border on the island of Ireland. And that just cannot be countenanced."
He said there has always been opportunity for resolution but said the problem is the British government has not been negotiating in good faith.
"Some of the things Jeffrey said are not fixable. He wants to turn back the clock. If he wanted to do that maybe he should not have backed Brexit in the first place."
Ulster Unionist Party (UUP) leader Doug Beattie said he is "certainly in solution mode" when it comes to approaching the ongoing issues with the Protocol.
Speaking on RTÉ's Drivetime, he said: "I think that the differences with myself, my party, and the Democratic Unionist Party is that we see the protocol as something which damages the Belfast Good Friday Agreement, it's not working as it should, but the way to fix that is through engagement by not withdrawing or disengaging.
"[Mr Donaldson] has now also threatened the stability of Stormont and that I don't think is a good thing either because you get to a cliff edge and when you fall off the only people who are going to suffer, are the people of Northern Ireland."