Sir Keir Starmer has said it is the moment to reset relations between the UK and the Republic of Ireland.
On Saturday, he became the first British prime minister to visit the Republic of Ireland in five years.
Downing Street said the visit marked a "new era of co-operation and friendship" between Britain and Ireland.
The prime minister held talks with Taoiseach (Irish Prime Minister) Simon Harris who was elected in April, just three months before his British counterpart - both are new to their roles.
Ukraine on agenda
After their talks, Sir Keir said there was a "huge amount of bi-lateral trade between our countries".
"I think £100bn / £120bn," he said. "That is why this is such an important relationship.
"Our economies, our markets are intertwined and have been for a very long time and so the foundation upon which we sort of base this reset is, I think, strong."
The two leaders also pledged to hold annual summits on trade and co-operation.
Mr Harris said he was "really delighted" that both leaders had had the "opportunity for an ambitious reset of the UK-Ireland relationship".
"We've had a very productive meeting with our teams and we've agreed on the importance of our responsibilities as co-guarantors of the Good Friday Agreement," he said.
"I'm also delighted that we've agreed a structure for engagement - an annual summit."
'Stand together'
The first summit is expected to be held in March and will discuss trade and security.
Sir Keir said pressing international issues including Ukraine and the conflict in Middle East had also been 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."
'New path'
Sir Keir Starmer arrived at Farmleigh House in Phoenix Park just before 13:00 local time.
He was met by Mr Harris who 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."
"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," he said
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 the reset in relations between the UK and Ireland "can be meaningful, it can be deep".
'Can we have Declan Rice back?'
Inside Dublin's 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 stadium.
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.
"It will make an appearance in my nine-a-side. This will be proudly worn in north London before too long," he said.
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?"
Speaking of the England footballer, he said: "No, absolutely not. He is fantastic."
'Our relationship has never reached its full potential'
Their full day of engagements in the Irish capital was topped off with their attendance at the Republic of Ireland v England football game at the Aviva Stadium in Dublin.
Although this is the first time Sir Keir has visited the Republic of Ireland in his official role as prime minister, it is not the first time the two leaders have met.
Mr Harris visited Sir Keir at Chequers, his country residence, 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.
Sir Keir 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 former 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.
From the scene: OceanNewsUK reporter Kevin Sharkey
A blazing sun against a clear blue sky wasn’t the only glow around the Phoenix Park today.
The mood music was beaming too, when the taoiseach welcomed the prime minister to the stately Farmleigh House.
Indeed, even before they arrived in separate cars, it was clear that the truculent post-Brexit nature of recent Irish-British relations was in their rear view mirror.
This was about looking forward positively.
Time to “reset” relationships, they proclaimed.
Reset - remember that word.
It’s not the first or last time we’ll hear it invoked, as this major political and diplomatic rebuild gathers pace.
“Céad Míle Fáilte”, said the taoiseach in his opening welcome remarks.
When he went on to explain that the greeting meant “a hundred thousand welcomes” in the Irish language, you could tell that Sir Keir was feeling the neighbourly political love.
For his part, the prime minister underlined their joint desire to “renew this relationship, deepen it”.
The setting for this meeting, the Phoenix Park, was not lost on some people.
The phoenix of Irish-British diplomatic relations, it seems, is rising again.