British Prime Minister Boris Johnson's attempts to replace the backstop have been dismissed as "fanciful".
Addressing an audience in New York, Tanaiste Simon Coveney said if the UK continues on its current path it will amount to "a disaster for Ireland".
He accused the UK government of "creating a much bigger problem to solve in the context of the Irish question".
As the House of Commons resumed, a defiant Mr Johnson insisted he will not back down in his demands for the backstop to be scrapped.
He claimed the EU "are now discussing a reopening of the Withdrawal Agreement" - something categorically ruled out by European leaders.
"I was told there was no chance of a new deal but we are discussing a new deal," Mr Johnson said.
There were heated scenes in the UK parliament as Mr Johnson's calls for an election were shouted down by opposition MPs who accused him of "lying and cheating".
The prime minister argued voters are being held captive by a "zombie parliament".
Asked whether he would respect legislation which requires him to seek a Brexit extension if no deal is secured, Mr Johnson replied: "We will of course obey the law and we will come out of the EU on October 31."
However, even if the PM is humiliated into asking the EU for another delay, there is no guarantee it would be granted.
Taoiseach Leo Varadkar said: "There's a lot of other European countries that are increasingly sceptical about whether there should be an extension or not.
"But I think we are a couple of weeks away from that scenario arising.
''Certainly, I would rather see a deal being ratified so that we can end the uncertainty that has been affecting citizens and business for far too long now."
As the chaos continued, the DUP called for tariffs to be applied on goods moving from the Republic into Northern Ireland if there is a disorderly Brexit.
MP Sammy Wilson said if the Republic puts checks in place then they must be replicated within the six counties.
The UK government has repeatedly stated that it will not create checkpoints regardless of the outcome of Brexit talks.
"The current approach by the government places Northern Ireland businesses at a disadvantage, will lead to a loss of tax revenue, make Northern Ireland a backdoor to Great Britain and alleviates pressure on the Republic of Ireland to reach a sensible deal,'' said Mr Wilson.
"This would be the same Irish Government which has displayed incredible intransigence throughout these negotiations."
The Irish Government has said it needs to protect its place within the EU Single Market by carrying out checks in a no-deal scenario.
British officials yesterday submitted another set of plans for how to maintain an open border without the backstop.
However, sources say the documents do not amount to a workable, legal alternative to the existing deal.
Mr Coveney challenged Mr Johnson to come up with a real solution.
He expressed frustration that Ireland is spending "hundreds of millions" to prepare for Brexit which is a "problem that is not of our making and that we disagree with".
He warned if a hard Brexit results in two different regulatory systems in Ireland "you have to have border infrastructures".
"We are spending a huge amount of money and a huge amount of time and effort and political currency across the European Union in trying to solve a problem that is not of our making and that we disagree with and don't see the sense of but respect because it was made democratically," he said.
Meetings between Irish and EU officials about the type of border checks that will be required in the event of a no-deal Brexit are continuing. It will take another "couple of weeks" before the plans are finalised.
Meanwhile, Mr Varadkar said the UK government had not submitted any new proposals in writing as of yet.
"Theresa May and her government were very much for a close relationship with the single market, a single customs territory.
''The new prime minister and his government are looking for a looser arrangement, something more akin to the relationship that the EU has with Canada.
"That actually makes the backstop all then more important and all the more necessary."