Ireland’s deputy prime minister has warned it will not be threatened into abandoning the backstop arrangement for the Irish border, comparing Britain’s latest Brexit moves to an ultimatum from someone threatening to jump out the window.

Simon Coveney said it was an “extraordinary situation” to see Theresa May negotiate a deal in good faith and then try to renege on it.

He said Ireland would not be beaten into accepting wishful thinking as a replacement to the Irish border backstop.

“You know unfortunately she has recommended that her party vote against the deal that she herself negotiated”, Coveney said.

“We have a deal, the British government was part of that. It’s an extraordinary situation that when a prime minister and a government negotiates a deal and then goes back and during the ratification process votes against their own deal, which is what happened yesterday, and now wants to go back to their negotiating partner and change everything.

“It’s like saying give me what I want or I’m jumping out the window. We owe it to the people of Ireland, north and south. We cannot approach this negotiation on the basis of threats.”

In a speech in Dublin, Coveney said no alternative arrangements that meet the threshold had been made. “We need a backstop or insurance mechanism based on legal certainty, and not just wishful thinking,” he said.

Ireland’s prime minister, Leo Varadkar, is expected to tell May in a telephone call later on Wednesday that she made a firm and solemn commitment to avoiding the return of a hard border in Ireland and that Ireland will insist she sticks to that.

Today Sean O'Rourke (@TodaySOR) 'It's like saying give me what I want or I'm jumping out the window' - Tánaiste Simon Coveney tells @TodaySOR the latest British Brexit moves are "extraordinary". #TodaySOR @RTERadio1 pic.twitter.com/7ui2oJeETV

Varadkar’s position is supported by the leader of Ireland’s main opposition party, Micheál Martin, who told BBC Radio 4 that Brexit transcended party politics.

Letters to the taoiseach released under the Freedom of Information Act also suggest public desire for defiance.

“For God’s sake, don’t be pressured in the coming weeks just because May is drowning. Let her fail for England’s sake as well,” one voter wrote.

Coveney expressed deep frustration over May’s U-turn in the face of pressure from hard Brexiters wanting to ditch the backstop.

He also expressed anger that Ireland had helped her win over EU colleagues in the negotiations to get her version of the backstop over the line, which involved a UK-wide customs arrangement, something Brussels was implacably opposed to until the last moment in negotiations.

“Ireland helped to lobby to change it [the original backstop]. Michel Barnier helped. She signed up for it, for her government to back it.

“The UK wants it both ways, no red lines and no backstop. We have a guarantee and we intend holding the British government to those guarantees. We had an agreement here. The prime minister signed up to it.”

“We have a negotiated outcome that is now not being followed through on. If you look at her interviews in recent weeks, she [May] talks about saying we can’t sit around and says we don’t want border infrastructure, we have to have legal and practical ways of doing that and that is why she defends the backstop.”

He said the Irish government was being asked to compromise on a solution that worked and replace it with wishful thinking.

Sources in Dublin say there is increasing anxiety about the prospect of no deal, but that there was an “air of calm, almost relief” on Wednesday morning due to the strength of unity shown by the EU immediately after the decision in the House of Commons to demand changes to the Irish backstop.

“The Irish position is in a way even less important than the EU position,” said Neale Richmond, spokesman for European affairs in the senate. “For the EU it is almost an existential question: ‘How can we let a member state which has a legitimate concern be overlooked in order to satisfy the demands of a state that is leaving the EU? How can we let an international peace treaty be compromised by a member state that is leaving?’”

While messaging from Dublin and Brussels has been highly co-ordinated throughout the last two years, there was comfort in Dublin that so many leaders across the EU had come out so strongly in their opposition to re-opening the withdrawal agreement.

“The Brexiters can’t just say it will be fine, ‘we won’t be putting up a border’. The point is once you have no deal you lose control,” said the source.