Taoiseach Simon Harris has spoken to British Prime Minister Keir Starmer and has accepted an invitation to meet in person in Downing Street on 17 July.
Mr Harris said that the call, held at around 8pm, included a commitment by both leaders to have a "close and constructive working relationship".
The Taoiseach said both he and Mr Starmer spoke of their "shared determination to reset and strengthen the bilateral relationship between Ireland and the United Kingdom".
Mr Harris confirmed this includes an invitation to meet Mr Starmer in Downing Street on 17 July, which he has accepted.
The Taoiseach also confirmed that during the phone call, the two leaders spoke about "legacy issues" in Northern Ireland and "the full operation of North-South and East-West Good Friday Agreement institutions".
He told Mr Starmer that he also welcomed the appointment of Hilary Benn as Secretary of State for Northern Ireland, and said a "meaningful reset" of the relationship between both countries "would require regular engagement".
Earlier, Tánaiste and Minister for Foreign Affairs Micheál Martin spoke to new UK foreign secretary David Lammy about the future relationship between Ireland and its nearest neighbour.
In a statement, the Tánaiste said both he and Mr Lammy agreed the Westminster election results offer a chance to rebuild bridges between both nations.
"We agreed that there is now a significant opportunity for a reset of our bilateral relationship. Now is a moment to embrace the spirit of partnership that we know can and does deliver for the people who call these islands home.
"We face challenges and we face opportunities, from the local to the global, from the Middle East to Ukraine, from positive UK engagement with the EU, to defending the multilateral order."
Mr Martin said the two 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."
Mr Lammy was appointed Foreign Secretary as new British Prime Minister announced his Cabinet.
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Sinn Féin leader Mary Lou McDonald said one of the biggest opportunities from the election was the opportunity for a reset of Irish-British relationships.
Speaking on RTÉ's Morning Ireland, she said: "I hope that Keir Starmer will avail of the political space and mandate that he has to repeal the legacy legislation and to reset that relationship.
"To honour the Good Friday Agreement in its totality and to work in real partnership with all of us to make life better for people in the North and right across the country."
Ms McDonald also said there was "real and lasting" damage in the North under Conservative rule.
"People here in the North really suffered under Tory austerity, the damage has been real and lasting and there will be a job of work ... to make the case for proper sustainable funding for public services in this part of Ireland," she said.
"That will be work for all of us."
