Tánaiste and Minister for Foreign Affairs Simon Coveney has said that this was a case of yet another Conservative Party leader losing leadership of the party because of their relationship with the EU.
“I feel sorry for Theresa May, she was doing her best for her country. Her resignation means a lot of uncertainty for Ireland,” he warned.
He told Newstalk’s Pat Kenny to show that Mrs May’s resignation was not a big surprise and that it remains to be seen whether the new Conservative party leader will have majority support in the House of Commons.
“We will have to see how divisive the Tory party leadership contest will be.”
Mr Coveney added that regardless of who is Prime Minister in the UK, the EU position on Brexit will remain the same.
As Prime Minister Theresa May had tried to compromise, she signed off on a deal to recognise the importance of Northern Ireland and the UK’s relationship with Ireland, “but her party and parliament did not recognise that.
“Even if the person in charge changes, the issues won't change, The EU will remain steadfast and supportive of Ireland’s position. The support they’ve shown has been quite extraordinary.
Mr Coveney said it was no secret that Boris Johnston wants to be Prime Minister, but he warned that there is a big difference between the priorities of the British public and the Conservative party with regard to Brexit.
“What’s on offer to the UK is fair and balanced.
“The idea that a new Prime Minister will be a tougher negotiator who will get a better deal – that’s not how the EU works.”
He said that from the EU perspective “patience has run out”. There are other issues that have to be urgently addressed such as budgets, migration, the rise of populism. “All of these things are going to be on the agenda for the new EU parliament.
“This is probably the most high profile European election ever held. For the other EU countries, Brexit is about sixth on their list of priorities.”
In the meantime, he said, Ireland is prepared for the worst case scenario – of a no deal Brexit. “I still think it can be avoided, but we have to be prepared in case politics fail us.”
Meanwhile, DUP leader Arelene Foster has paid tribute to Theresa May saying "we enjoyed a respectful and courteous relationship".
She said: "I commend and thank the Primer Minister for her dutiful approach on national issues and her willingness to recognise Northern Ireland's need for additional resources through Confidence and Supply arrangements."
Ms Foster added: "I pay tribute to her selfless service in the interest of the United Kingdom and wisher well for the future."
Taoiseach Leo Varadkar has paid tribute to British Prime Minister Theresa May following her announcement that she will resign on June 7.
In a statement, the Taoiseach said he got to know her very well over the last two years.
"She is principled, honourable, and deeply passionate about doing her best for her country, and her party," he said.
"Politicians throughout the EU have admired her tenacity, her courage, and her determination during what has been a difficult and challenging time."
He added that Mrs May "strove to chart a new future for the United Kingdom."
Mr Varadkar said he wishes Mrs May well for the future and looks forward to "working closely" with her successor.
Fianna Fáil leader Micheál Martin responded to the resignation of Mrs May saying that it was a very difficult day for the British PM "at a personal level".
He said: She has committed her life to public service and has had responsibility for leading the very highest offices in British life."
Mr Martin said that Mrs May's fate was a "reflection of the emerging and ongoing crisis in British politics as a result of Brexit."
Mr Martin added he wishes Mrs May well for the future.
Meanwhile, Brendan Howlin called for Ireland to move to an ‘Orange Warning’ as politics in the UK will be unstable for a time, especially following the EU elections there.
Mr Howlin said: “The resignation of Prime Minister Theresa May represents the exhaustion of the current political process around Brexit. It is now clear that the negotiated withdrawal agreement and political declaration are dead in their current form."
The Labour leader said that while Mrs May's resignation represents change, without "clear, strong leadership" there is a risk of "chaos".
He added: “Our own Government should do everything in their power to persuade the next British Government to consider a new public vote and to set out the case for remaining inside a reformed and renewed European Union.”