UK Prime Minister Keir Starmer and Irish premier Simon Harris have committed to reset and strengthen Anglo-Irish relations “with urgency and ambition”.
The Taoiseach “warmly congratulated” Sir Keir on his appointment and said he looked forward to having a “close and constructive” working relationship.
Mr Harris also accepted an invite to visit Downing Street on July 17.
“The Taoiseach and the Prime Minister spoke of their shared determination to reset and strengthen the bilateral relationship between Ireland and the United Kingdom and to set about that task with urgency and ambition,” a statement said.
“They discussed Northern Ireland, welcoming the restoration of the institutions, including the full operation of North-South and East-West Good Friday Agreement institutions, as well as legacy issues.”
Northern Ireland First Minister Michelle O’Neill and deputy First Minister Emma Little-Pengelly spoke by phone with Sir Keir on Friday where they congratulated him.
Ms O’Neill said she raised the need to “reset” British-Irish relations, funding public services, the redevelopment of Casement Park and the Legacy Act.
“I urged the Prime Minister to follow through on his commitments to bin the Tories’ shameful Legacy Act which has failed victims and survivors,” Ms O’Neill said.
“I will continue to press the British government on the things that matter most people, delivering for public services and all our communities as we engage in the days ahead.”
Ms Little-Pengelly said: “We raised a number of key issues including the importance of investment to ensure fiscal stability for Northern Ireland.
“We also spoke about the benefits of a building a positive working relationship and strengthening the links between the NI Executive and the UK Government moving forward.”
Ireland’s deputy premier Micheal Martin said the Anglo-Irish relationship was both rich and important, after speaking with the newly appointed British Foreign Secretary David Lammy on Friday.
Mr Martin, who is Minister for Foreign Affairs, said the new UK government offered a “significant opportunity” and that there was much to discuss.
The relationship between London and Dublin has been under severe strain in recent years.
The turbulence caused by Brexit and the Conservative government’s controversial laws to deal with the legacy of the Troubles were areas of major tension.
Sir Keir has pledged to repeal the legislation that offered conditional immunity for perpetrators of Troubles crimes.
“Today is about looking forward,” Mr Harris said at Dublin’s Government Buildings on Friday morning.
“It’s about realising the full potential of that relationship between Taoiseach and Prime Minister and between our governments.
“I know that Keir Starmer and I share a desire for it to go from strength to strength. It is time for a great reset.”
Mr Martin said: “I was pleased to speak this evening with the new UK Foreign Secretary David Lammy and to congratulate him on Labour’s election victory and his appointment to his new role.
“We agreed that there is now a significant opportunity for a reset of our bilateral relationship.
“There is much for us to discuss and I am looking forward to engaging on all these issues with the Foreign Secretary over the period ahead.
“Our countries share a relationship that is as rich as it is important. We are near neighbours with close cultural connections. We are significant trading partners with countless family ties, reaching across these islands.
“Most critically, together, the British and Irish governments are co-guarantors of the Good Friday Agreement. I look forward to building on that foundation to ensure positive progress together and to take forward our shared agenda.”
On Thursday evening, DUP leader Gavin Robinson said Sir Keir “is somebody we have a good relationship with”, calling Labour’s victory an “extraordinary” outcome.
Sinn Fein leader Mary Lou McDonald said that she hopes “this new horizon is grasped by the Labour Party”, adding “there’s a lot to be repaired”.
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