Tánaiste and Minister for Foreign Affairs Simon Coveney has said it would be the UK's choice whether or not it wants to leave the EU without a deal and everyone in the EU is in trouble if the new British prime minister wants to tear up the Withdrawal Agreement.
Speaking on the BBC's Andrew Marr show, he said: "If the approach of the new British prime minister is that they're going to tear up the Withdrawal Agreement, then I think we're in trouble, we're all in trouble, quite frankly, because it's a little bit like saying: 'Either give me what I want or I'm going to burn the house down for everybody'."
He added: "The EU has made it very clear that we want to engage with a new British prime minister, we want to avoid a no-deal Brexit."
Mr Coveney said the backstop can be avoided by negotiation, but that it needs to be part of the Withdrawal Agreement.
"The idea that we can consider moving away from something that took two-and-a-half years to negotiate given all of that complexity and compromise on both sides to try and accommodate British red lines, don't forget, not EU red lines, we're simply not going to move away from the Withdrawal Agreement," he said.
Mr Coveney said leaving the EU without a deal would be a "British choice" determined by the new prime minister and the House of Commons.
He said Ireland and the remaining EU member states want to resolve the issues to avoid a no-deal scenario, but will not do so on the basis of being told what must happen.
"Everybody loses in a no-deal Brexit scenario," he said.
"If the House of Commons chooses to facilitate a no-deal Brexit and if the new British prime minister chooses to take Britain in that direction, then it will happen. But this will be a British choice, not an Irish choice, not an EU choice, this is a British choice."
Mr Coveney also insisted that the EU is united in its support for the backstop - the insurance mechanism to ensure a hard border is not reinstated between North and South - and is "not going to change from that position."
He said: "Any international negotiation needs to involve compromise on both sides. We have a deal that has involved compromise on both sides to facilitate British red lines throughout this process and a new British Prime Minister does not change that.
Mr Coveney said checks would have to be carried out on the island of Ireland in the event of a no-deal Brexit, but he said those checks would not be at the border.
"We have to protect relationships and peace on the island of Ireland, and we are not going to create a security risk by putting a border in place on the border, but we also have to make sure that there are verification mechanisms to ensure what the EU knows what is coming into its single market".
He added: "There will need to be checks somewhere. We are working out with the European Commission how that will work. "
He said the Government had always made it clear that if the British government "forces a no-deal Brexit on everybody" then the Republic would have "no choice" but to protect its place in the EU single market.
However, he said such a scenario would "fundamentally disrupt" the all-island economy.
Meanwhile, Brexit Secretary Steve Barclay said he told the EU that it is difficult to envisage how the Withdrawal Agreement will pass the Commons if nothing is changed.
"The current text of the Withdrawal Agreement - if nothing at all is changed - then I didn't see that going through the House of Commons," he told Sky's Sophy Ridge on Sunday.
"It's been rejected three times and since then we've had the European elections where, if anything, the House has further polarised, and so what I was very openly and honestly sharing with them was an update on the political scene in England.
"I think if the text isn't changed in any way, then it is difficult to envisage how that will go through the House of Commons."
No-deal would 'devastate' NI's economy
Writing in the London Edition of the Sunday Times, Mr Coveney said a no-deal Brexit would devastate Northern Ireland's economy.
He said the backstop exists to protect the Good Friday Agreement and warned that nothing should be done to put the peace on this island at risk.
In a stark assessment of what a no-deal would mean, Mr Coveney said Northern Ireland has more to lose from such a scenario than anywhere else.
He said it would devastate the North's economy with tariffs and rules that would fundamentally disrupt the all-island economy on which so much progress has been built.
My Coveney referenced comments by the recently appointed chief constable of the PSNI who warned a hard Brexit would have an absolutely detrimental impact on the peace process.
He said the Irish Government is looking forward to meeting and engaging with the new prime minister.
But with just 100 days between that appointment and the day Britain is due to leave the EU, he urged the new PM to be realistic and honest about the impact of their decisions.
Additional Reporting PA