King Charles and Liz Truss met on Sunday afternoon as hundreds of dignitaries from across the globe descend on London to pay their respects to the Queen.
The prime minister spent a second day in informal meetings with heads of government and state at Downing Street ahead of a planned reception at Buckingham Palace.
She has concluded meetings with Canadian prime minister Justin Trudeau and Ireland's Taoiseach Micheal Martin, and has also met with Polish president Andrzej Duda.
But a planned bilateral with US president Joe Biden was cancelled and the pair will instead talk at an upcoming UN general assembly session next week.
Yesterday Ms Truss had informal talks held with the Australian and New Zealand prime ministers Anthony Albanese and Jacinda Ardern at the government’s hevening country house in Kent.
Taoiseach Mr Martin said the meeting with Ms Truss has been "warm" but that he had refrained from discussions about the controversial Northern Ireland protocol.
"I don't think this is the time, if you don't mind me saying so, to get into the detail about issues like the protocol," he told BBC Radio 4's Today programme.
"I've had a good telephone conversation last week with the British Prime Minister, had an initial warm meeting this morning where we discussed many issues in the context of the British-Irish relationship.
"But I do thing the opportunity is there for us to reset relationships and to be conscious of what we achieved in previous years, the obstacles that were overcome then.
"And that gives us the strength to know that we have the capacity to overcome current obstacles, current issues that potentially could impede the relationship, and I believe we can overcome them."
However, Irish public broadcaster RTE reports, that the pair agreed there was still an opportunity for a negotiated outcome on issues around the protocol.
Downing Street said on Sunday night that the meetings “were an opportunity for the Prime Minister and key leaders to reflect on the life and important global role of Her Majesty The Queen, and to reaffirm the strength of our diplomatic relationships”.
