Alternatives to the border backstop represent "wishful thinking", the Tánaiste has said.
Simon Coveney said many hours were involved in coming up with a "legally credible and pragmatic" solution.
He asserted the draft backstop text rejected by British MPs already allows the EU and UK to work on alternative arrangements.
Mr Coveney said: "The Irish protocol in the Withdrawal Agreement already allows for alternative arrangements or alternative solutions to the backstop and if they're there they can replace the backstop.
"The problem is that none of those ideas around alternative arrangements stand up to scrutiny, we have certainly not seen any that have."
Mr Coveney attended meetings in Brussels on Monday.
He added: "What Ireland is being asked to do by some in Westminster is to essentially do away with an agreed solution between the UK government and EU negotiators and to replace it with wishful thinking and I think that's a very unreasonable request to ask the Irish Government to be flexible on.
"So if there are alternative arrangements that can work the current protocol, if people take the time to read it, takes account of that and it says very clearly that the backstop can be replaced by alternative arrangements as long as they work."
The Irish Government has strongly supported the concept of a backstop in the face of criticism from Northern Irish unionists and Tories at Westminster.
Unionists fear it could undermine the constitutional integrity of the UK by creating a distinct customs regime for Northern Ireland.
Nationalists argue that a hard Brexit without a backstop could endanger peace process gains and would create trade chaos in Ireland.
Mr Coveney added: "We have a pragmatic solution that we know will work, it was agreed with the British government and we expect them to follow through on that commitment."