The government has said the UK needs to come up with alternative solutions if it will not support the EU's legal document on Brexit.
Brussels chief negotiator Michel Barnier's text outlining a default scenario for regulations on an all-Ireland basis has drawn ire from Theresa May.
But Taoiseach Leo Varadkar said he would prefer to see what is being classed as "Option A" - a new relationship between the UK and EU that is so close that a border is unnecessary.
"Hardline Brexiteers and some politicians in Northern Ireland will say 'No' and will be angry at what they see today, but just saying 'No' and being angry is not enough," the Taoiseach told the Dail.
"If people do not like what they see today, it is incumbent on them to come up with alternative solutions and to flesh out option A and option B, write it down in a legal form that can be enforced and then we can negotiate on that."
Foreign Affairs Minister Simon Coveney said the Irish Government had insisted on a backstop or default position in the absence of a better deal so far.
"This is not trying to provoke, it's not trying to reinterpret," he said.
Mr Barnier's legal text sparked claims in some political circles in Britain that the EU was attempting to annex Northern Ireland.
Democratic Unionist leader Arlene Foster tweeted after the publication of the EU document and said it was "constitutionally unacceptable & would be economically catastrophic for Northern Ireland".
EU draft text is constitutionally unacceptable & would be economically catastrophic for Northern Ireland. I welcome the Prime Minister's commitment that HMG will not allow any new border in the Irish Sea. Northern Ireland must have unfettered access to GB market. AF— Arlene Foster #We’llMeetAgain (@DUPleader) February 28, 2018
Mr Coveney said Ireland deserves to know that in the absence of an agreement between the UK and EU on trade and customs post-Brexit, that a border will not be recreated on the island.
And reacting to the British PM's statement in the House of Commons, he said: "The constitutional integrity of Northern Ireland and indeed the relationship north and south on the island of Ireland is essentially subject to the Good Friday Agreement.
"Nobody is looking to pick a fight here."
Today's EU draft text is absolutely faithful to the political Agreement in December an should not be a surprise to anybody https://t.co/mk23mUIXJw— Simon Coveney (@simoncoveney) February 28, 2018
Mr Coveney said nobody should be surprised by the legal document and that it was simply a legalistic text of what was agreed in December.
"The Irish Government has made it very clear that we're not hardening our position," Mr Coveney said.
"We are simply holding our position."
Mr Coveney said Ireland was insisting on a default clause in the legal text in the absence of solutions or suggestions from Mrs May's Government.
He added: "Until we get that clarity well then we of course have to hold on very tight to that position because it's all we've got."
Sinn Fein president Mary Lou McDonald launched a tirade over the reaction from the British Government and the DUP to the EU legal text.
"The Tory-DUP axis is satisfied to treat the welfare of the people of this island as collateral damage so long as they achieve their 'little Englander' vision for Brexit," she said.