Measures proposed by the UK to replace the backstop do not yet come close to what is needed and it is possible that no solution exists, the Tánaiste has said.
British Prime Minister Boris Johnson told European Commission President Jean-Claude Juncker by phone today that there was no prospect of a Brexit deal unless the backstop was abolished, his office said.
"The Prime Minister set out that the UK will be leaving the EU on October 31 whatever the circumstances, and that we absolutely want to do so with a deal," a spokeswoman said.
"The PM was also clear however that unless the Withdrawal Agreement is reopened and the backstop abolished there is no prospect of that deal."
Earlier, Tánaiste and Minister for Foreign Affairs Simon Coveney said: "I think we need to be honest here, that the alternative arrangements that have been discussed to date do not do the same job as the backstop, not even close."
Mr Coveney made the comments at a news conference in Prague following a meeting with Czech Foreign Minister Tomas Petricek.
"So let's not pretend that solutions exist when they might not," he said.
Ireland is, however, open to further suggestions and wants to find a deal, said Mr Coveney.
"Our message is simple: We want to work this out.
"There needs to be a deal done on the basis of honesty, in terms of the complexity of the issue we are facing."
The British government's Brexit negotiator, David Frost, is due in Brussels tomorrow to discuss the border issue with the European Commission as British opposition parties try to unite to stop any no-deal departure from the EU on 31 October.
Meanwhile, a report in the Wall Street Journal suggests that Mr Johnson intends requesting a series of agreements which would keep the UK or Northern Ireland aligned to EU rules.
The initiative would reduce the need for infrastructure on the border and allow the UK to pursue a free trade agreement with other countries, according to the newspaper.
In response, Mr Coveney said: "The Withdrawal Agreement already allows for the backstop to be overwritten."
He added: "However, these alternatives have to be legally sound and with no border infrastructure or related checks."
A British government spokeswoman said the UK is working "at pace to find a wide range of flexible and creative solutions" for the border post-Brexit.
She said: "We are ready to negotiate in good faith an alternative to the backstop with provisions to ensure the Irish border issues are dealt with where they should always have been: in the negotiations on the future agreement between the UK and EU."
Last month a report by the Alternative Arrangements Commission, a group led by senior Conservatives suggested a new shared food safety and animal health area encompassing the island of Ireland and the island of Britain as a whole should be created to prevent the backstop from taking effect.
It said that such an arrangement would remove the need for customs, food safety and animal health checks between north and south, or between the island of Ireland and Britain.
Mr Johnson has described it as an "excellent" paper.
However, Irish officials have flatly dismissed the idea as tantamount to Ireland having to leave the EU's single market for agriculture and food safety.
Additional reporting: David Murphy