The First Minister of Northern Ireland Peter Robinson praised US Secretary of State Hillary Clinton for her "instrumental" role in the peace process.
He said: "Very often, we will sit down, and somebody will mention someone who has claimed to be instrumental in the peace process, and Martin and I look at each other, and say 'Do you know them?'
"But you are one person who has consistently helped us. You have been a great friend to Northern Ireland."
Referring to the assassination off Co Sligo in the Irish Republic, he said he told the royals that he recognised they had lost a relative.
"I said to the Queen and the Duke they too had lost a loved one," he said.
Mr McGuinness revealed some of the detail of the private meeting during a talk show on RTE television.
The killing was discussed briefly after an historic handshake between the pair which has been hailed as a watershed moment in Anglo-Irish relations.
Mr McGuinness has not discussed any of the detail of the meeting until now. When he left the theatre he would only say that the Queen was very nice and that he was still a Republican.
Sinn Fein chief Martin McGuinness told the Queen that he recognised she suffered loss in the Northern Ireland Troubles.
The Stormont Deputy First Minister revealed that he addressed the 1979 IRA murder of her cousin Earl Mountbatten when he met her privately in Belfast last Wednesday.
The former terror commander said the Queen was very gracious about what he said.
Mr McGuinness said he would not detail exactly what he said during the eight minute discussion in the Lyric Theatre, which the Duke of Edinburgh also attended, or how the Queen responded.
The Queen and the Duke of Edinburgh were met by cheering crowds as they travelled in an open-top car to The Parliament Buildings in Stormont, as part of her visit to Northern Ireland.
Martin McGuinness has described meeting the Queen as, "very nice."
Martin McGuinness has said that, "it was nice" to meet the Queen and that the meeting went, "very well" as he left the Lyric Theatre this afternoon.
He also added, "I'm still a Republican."
Northern Ireland Secretary Owen Paterson met Mr McGuinness this morning and added that he was relaxed.
He said the Deputy First Minister greeted the Queen in Irish and their meeting was cordial.
It had obviously gone very well.This will move Northern Ireland on to a whole new plane. After all the trauma of Northern Ireland, everyone is looking forward.It is about a shared future, not a shared-out future.
None of this could have happened a few years ago so it is all looking to the future.
He said it was absolutely appropriate that when the Queen visits parts of the UK, she meets local politicians, democratically elected, pursuing their democratic political goals by peaceful means.
Mr Paterson added that it built on the success of the Queen's visit to the Republic of Ireland last year.
The Queen is expected to visit Stormont later today.
It is understood that during the VIPs' initial private meeting, Mr McGuinness welcomed both the Queen and President Higgins in Irish.
The Deputy First Minister is said to have commented briefly on the Queen's visit to Dublin last year, and in particular her comments regarding all the victims of the conflict.
A Sinn Fein spokesman said: "He emphasised the need to acknowledge the pain of all victims of the conflict and their families."
Mr McGuinness is said to have spoken to the Queen of the significance of her visit, and of the need for it to be built upon in the time ahead.
Sinn Fein said Mr McGuinness told the Queen that their meeting was a "powerful signal that peace-building requires leadership".
The Deputy First Minister also praised the role of the President in today's encounter, and welcomed that the engagement took place at an event celebrating culture across Ireland.