Sir Keir Starmer has become the first British prime minister to visit the Republic of Ireland in five years.
Downing Street said Saturday’s visit marks a “new era of co-operation and friendship” between Britain and Ireland.
The prime minister has met Taoiseach (Irish Prime Minister) Simon Harris, who was elected in April just three months before his British counterpart – both are new to their roles.
Their full day of engagements in the Irish capital is being topped off with the Republic of Ireland v England football game at the Aviva Stadium in Dublin.
Mr Harris wished Sir Keir “a hundred thousand welcomes” as the two leaders shook hands.
The taoiseach, who described Sir Keir as his friend, said: “It’s a really great honour to host you here today on your first official visit to Ireland as prime minister.”
He added: “We both said we wish to really place British-Irish relations on a new path and I really appreciate the time that you’ve given to us since taking office, and I’ve tried to respond in kind.”
Mr Harris said a reset in relations had to be embedded in “peace and prosperity, mutual respect and friendship”.
He said their “most solemn duty” as leaders of the UK and Irish governments was as co-guarantors of the peace process in Northern Ireland.
Sir Keir said it was the “moment for reset” of relations between the UK and Ireland.
“That reset, I think, can be meaningful, it can be deep,” the prime minister said.
“Of course, it covers the relationship between our two countries. Obviously it has to cover the Good Friday Agreement and I take very seriously our joint role in relation to that.”
Ukraine on agenda
Sir Keir said pressing international issues including Ukraine and the conflict in Middle East were also on the agenda for the meeting.
“In the face of Russian aggression, we have to stand together, to co-ordinate, stand with our allies and give Ukraine all the support that it needs for as long as it needs,” he said.
“In relation to the Middle East, we need a ceasefire so that the remaining hostages can come out, so that desperately-needed aid can get in to Gaza, and that we can step down the path towards a two-state settlement, which in my view is the only lasting settlement that will bring about lasting peace.”
At the scene: Kevin Sharkey BBC News NI
The sun came out above Phoenix Park as the Prime Minister arrived here at Farmleigh House just before 1pm.
Sir Keir Starmer and the Taoiseach Simon Harris had a brief chat at the steps – their words drown out by the sound of an overhead helicopter, much to the frustration of curious members of the media waiting nearby.
Then, a quick pose and handshake for the cameras before the two leaders went inside to resume their efforts to rebuild damaged diplomatic relations.
‘Can we have Declan Rice back?’
Inside Farmleigh House, Sir Keir signed the visitors’ book.
They moved into the walled garden at the property, where they walked together in conversation.
A young boy who received medical treatment in the UK presented the two leaders with Irish and English football scarves to swap before the clash at the Aviva later.
They also swapped football jerseys.
Sir Keir held up an Irish shirt with his surname on the back and laughed when asked if he would wear it to the match later.
He said: “It will make an appearance in my nine-a-side. This will be proudly worn in north London before too long.”
Looking at his England shirt with “Harris” on the back, the Taoiseach joked: “I never thought I’d see my name on anything.”
Meanwhile, Sir Keir said “absolutely not” to a shout of “can we have Declan Rice back?”
He said: “No, absolutely not. He is fantastic.”
‘Our relationship has never reached its full potential’
Sir Keir and Mr Harris met in Chequers in mid-July after Labour’s general election victory.
They discussed divisions over the UK Legacy Act, and they were photographed having a pint of Guinness.
The taoiseach was the first international leader hosted by Sir Keir after coming to power, a fact said to demonstrate the prime minister’s personal commitment to a strong UK-Ireland relationship.
Saturday’s visit comes after the prime minister’s visit to Berlin and Paris last week to continue the UK’s reset with its key European partners.
The prime minister and the taoiseach will also meet Irish business leaders to encourage enhanced bilateral trade and investment in pursuit of growth.
The last British prime ministerial visit to the Republic of Ireland was by Boris Johnson, in September 2019.
In recent times, under the Conservative government, relations between the UK and Ireland were said to be at their lowest ebb in decades because of differences over Brexit.
Ireland also launched an international legal case against Britain over the Legacy Act which Sir Keir has now promised to repeal.
Analysis: Gareth Gordon, BBC News NI political correspondent
This visit, with its sporting conclusion, takes political football to a new level.
And as the cliché goes it really is a game of two halves.
Under Leo Varadkar and Boris Johnson relations between the two countries reminded some of that famous commentary line “they think it’s all over – it is now”.
Then, Sir Keir Starmer walks onto the pitch and it seems to be a whole new ball game.
On both the main issues the two countries have clashed over in recent times the Labour administration coming to power may herald a new beginning.
Certainly the mood music is much better.
In 1995, the England football team played in Dublin, however the “friendly” had to be abandoned after visiting fans rioted.
A much different result is expected 29 years on, whichever side wins the football.