Taoiseach Simon Harris will meet the new British Prime Minister Keir Starmer in London later this month.
The two leaders spoke by phone on Friday following a landslide victory for the UK Labour Party in the country's general election.
Mr Harris warmly congratulated Mr Starmer on his appointment and "historic electoral victory".
The Taoiseach said he looked forward to having a close and constructive working relationship.
The two leaders also 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".
British Prime Minister Keir Starmer walks back after speaking to the media outside 10 Downing Street in London, 5-7-24. Image: Associated Press/AlamyMr Starmer invited Mr Harris to meet him in Downing Street on July 17th and the Taoiseach accepted.
They also discussed Northern Ireland as well as legacy issues, while the Taoiseach welcomed the appointment of Hilary Benn as Secretary of State for Northern Ireland.
The leaders agreed a closer relationship between Dublin and London was needed and "a meaningful re-set would require regular engagement between them".
They agreed to start work on that immediately and to stay in close contact.
'Reset in Anglo-Irish relations'
Speaking after the call, Mr Harris said now is an important moment.
"I was very pleased to have an opportunity to speak with the British Prime Minister Keir Starmer to congratulate him on his election and to accept his invitation," he said.
"I think this presents a really important moment for the reset that we must see in Anglo-Irish relations.
"I know from the call that we had both he and I are determined to lead in relation to that.
"The British-Irish relationship is so important for citizens on our island and across our islands - and now I believe we have an opportunity to make real progress," he added.
Tánaiste Micheál Martin earlier spoke with Britain's new Foreign Secretary David Lammy and Northern Ireland Secretary Hilary Benn.
