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.
Today's handshake between the Queen and former IRA commander Martin McGuinness is a historic gesture of peace. Here are some others.
The hands of history? The Queen and former IRA Commander Martin McGuinness will make a remarkable gesture for peace today.