Northern Ireland Deputy First Minister Martin McGuinness has described his meeting with Queen Elizabeth as highly significant and symbolic.
Speaking at a Sinn Fein event in Westminster, McGuinness said it could help define "a new relationship between Britain and Ireland and between the Irish people themselves."
A former IRA commander, McGuinness made history on Wednesday during a meeting at which him and Queen Elizabeth shook hands, as part of the Queen's two-day visit to Northern Ireland.
This week's symbolic event has been hailed as a watershed moment in the peace process.
The handshake was public and occurred at a theatre in south Belfast. During his parting words McGuinness told the Queen in Gaelic: "Goodbye and God's speed."
The MP said the meeting at the Lyric Theatre in Belfast "came about as a result of decades of work constructing the Irish peace process."
"I was, in a very pointed, deliberate and symbolic way, offering the hand of friendship to unionists through the person of Queen Elizabeth for which many unionists have a deep affinity," he said.
"It is an offer I hope many will accept in the same spirit it was offered."
He said the issues between Britain and Ireland have not been resolved but "we now operate in a new context of compromise, agreement and peace."
During his address McGuinness expressed remorse regarding the troubles.
"I genuinely regret every single life that was lost during the conflict, and today I want every family to know that your pain is not being ignored," he said.
He added that the "task of building national reconciliation is as much a part of the peace process as anything that has gone before".
He called on the Orange Order to begin dialogue with Sinn Fein and nationalist residents.
He said they needed to "seriously debate how they are going to step forward and make their contribution to a lasting peace in the coming weeks".
Thursday’s event was attended by Sinn Fein MPs Michelle Gildernew, Pat Doherty, Conor Murphy and Paul Maskey. Sinn Fein TD for Dublin South Central, Aengus O Snodaigh.
Read the full text of his speech here.