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.
Ciaran Cunningham from the Republican Network for Unity has spoken to ITV News' Royal Correspondent Tim Ewart about the handshake between Martin McGuinness and the Queen.
Mr Cunningham said that, "Martin McGuinness is playing with words," when he says he is still a republican.
Ciaran Cunningham from the Republican Network for Unity has said that:
Martin McGuinness has lost all logic and he lost all sense and he has lost all respect.
Martin McGuinness is playing with words, he's trying to make the word Republican mean something that it doesn't mean.
The Queen publicly shakes the hand of former IRA member Martin McGuinness in an historic moment in Belfast.
The Queen has shaken hands in public with Sinn Fein's Martin McGuinness in a gesture of reconciliation.
Mr Guinness held the monarch's hands for a few moments, spoke to her in Irish and told her the words meant: "Goodbye and God's speed."
Asked how David Cameron viewed the handshake, the Prime Minister's official spokesman said:
Clearly, there was a visit by Her Majesty to the Republic of Ireland last year. That has taken relations between the two countries to a new level.
We think it is right that the Queen should meet representatives from all parts of the community.
In an historic encounter, the Queen has shaken the hand of Sinn Fein's Martin McGuinness.Read the full story ›
The Queen has shaken the hand of Sinn Fein's Martin McGuinness in an historic encounter that would have seemed unthinkable just a decade ago.
They met behind closed doors in a room within Belfast's Lyric Theatre during an event celebrating the arts in the Republic and Northern Ireland.
In a quiet space used by the Lyric for creative learning, the two were joined by the Duke of Edinburgh, Northern Ireland first minister Peter Robinson, Irish President Michael D Higgins and his wife Sabina.
Called the McGrath Suite, named in honour of benefactor Harvey McGrath, the former chairman of the British insurer Prudential, and his wife Allison, the room is usually filled with toddlers enjoying story telling sessions or drama students taking part in workshops.
Today it was sparsely furnished with leather seating - four chairs and a sofa - set around a round wooden table decorated with flowers, with refreshments of tea, coffee and still and sparkling water on a side table.
The floor-to-ceiling windows, which look out on to landscaped gardens and the River Lagan, were covered with curtains.
Security is tight around the theatre in Belfast where the Queen will meet Martin McGuiness shortly.
As well as an ambulance and police officers on the street police are also visible on the roof of the Lyric Theatre.
Road blocks near where Martin McGuinness and the Queen will meet soon.