Taoiseach Leo Varadkar has warned that we are now entering a new phase of Brexit and one that may be very dangerous for Ireland.
His comments come in the wake of Theresa May's announcement that she will step down as Conservative Party leader on 7 June.
Mr Varadkar said: "we may see the election of a euro-sceptic prime minister who wants to repudiate the withdrawal agreement and go with a no deal."
He also said we may see a new UK government that wants to see a closer relationship with the EU and go for a second referendum.
Earlier, Tánaiste and Minister for Foreign Affairs Simon Coveney said: "From my perspective, I don't see the European Union offering any new prime minister a better or very different deal to what was on offer to Theresa May.
"This idea that a new prime minister will be a tougher negotiator and will put it up to the EU and get a much better deal for Britain? That's not how the EU works."
The European Union's position on the terms of Britain's exit from the bloc has not changed despite Mrs May announcement, Commission spokeswoman Mina Andreeva said.
"President Juncker followed Prime Minister May's announcement this morning without personal joy," she told a news briefing.
"The President very much liked and appreciated working with Prime Minister May.
He will equally respect and establish working relations with any new prime minister, whomever it maybe.
"Our position on the withdrawal agreement - there is no change to that," Ms Andreeva said.
She reiterated the bloc would not change the stalled Brexit withdrawal deal but could tweak the accompanying political declaration on EU-UK ties after Brexit.
The EU's chief Brexit negotiator Michel Barnier tweeted his reaction to Mrs May's resignation.
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