Prince Charles expressed his "regret" over lives lost in in Northern Ireland's Troubles during a private meeting with Gerry Adams.
The Sinn Fein president spoke to Charles about the 1979 IRA bombing in which his great uncle Lord Mountbatten was murdered.
Adams said: "Both he and we expressed our regret for what happened from 1968 onwards.
"We were of a common mind and the fact that the meeting took place, it obviously was a big thing for him to do and a big thing for us to do."
Gerry Adams has said Sinn Fein wants to deal with the past - but is waiting for the British Government to rise to the challenge.
Speaking after his historic meeting with Prince Charles, he said: "We are up for that challenge and will deal with it in a very forthright and honest way."
Gerry Adams has said he and Prince Charles put the past behind them today to concentrate on "moving towards the future".
Speaking to reporters after their private discussion following their much-publicised handshake, the Sinn Fein leader said: "I think it was a good meeting.
"We discussed the need for the entire process to move forward in terms of people who have suffered, families who have been bereaved, and the need to heal.
"To have relationships between the people of these islands and of this island, moving towards the future."
Adams said Prince Charles told him he had reflected on his own suffering which the royal said he "given him an affinity and understanding of other people."
He added: "The war is over. We need to be mindful of all that happened in that 30 year stretch. Now, while being totally mindful of the victims, we need to be looking towards the future.
"And it's fair to say that Prince Charles is also looking to the future and wants to be an influence on that."
In an historic moment Prince Charles has shaken hands with Gerry Adams in Galway.
The prince is starting an emotional and historic trip to the west of Ireland where his great uncle Lord Louis Mountbatten was assassinated by the IRA.
At a welcome reception at the National University of Ireland the Prince of Wales and Duchess of Cornwall were seen in the same place as Gerry Adams for the first time.
However there was a great deal of distance between the royal couple and the Sinn Fein leader was difficult to pick out at the back of the crowd.
Prince Charles will meet Gerry Adams face to face today as he begins an emotional and historic trip to the west of Ireland where his great uncle Lord Louis Mountbatten was assassinated by the IRA.
Gerry Adams has refused to confirm if he will apologise to Prince Charles over the death of Lord Mountbatten when he meets the royal later today.
The Sinn Fein President said that "one couldn't help but be regretful about the loss particularly when there are children involved."
Lord Louis Mountbatten was the great-uncle of Prince Charles and was killed by an IRA bomb in Classiebawn Castle in Mullaghmore, Country Sligo, his 14-year-old grandson Nicholas Knatchbull and Paul Maxwell, a 15-year-old crew member were also killed.
- Read more: What happened to Lord Mountbatten?
Speaking about meeting the Prince of Wales Mr Adams said:
I don't have any expectations other than this being an engagement which I hope symbolically and practically will assist the entire process.
Mr Adams told reporters that he was expecting that he would shake hands with the Prince.
Sinn Fein requested the meeting between Prince Charles and Gerry Adams ITV News understands.
Although the Prince has previously met Martin McGuiness, today will be the first time he has met the President of Sinn Fein.
The Prince of Wales is making an historic trip to the west of Ireland where his great uncle Lord Louis Mountbatten was assassinated by the IRA.
The great-uncle of Prince Charles was killed along with his 14-year-old grandson and two others in an IRA bomb blast in August 1979.Read the full story ›
An anticipated historic meeting between Sinn Fein leader Gerry Adams and Prince Charles has been hailed in some quarters as the next phase in deepening the bonds between the UK and Ireland.
The meeting with Mr Adams will take place before Prince Charles visits the site of his great-uncle Lord Louis Mountbatten's murder and is a way of "promoting reconciliation and healing", according to a Sinn Fein party official.
Lord Mountbatten was assassinated by the IRA along with Lady Doreen Brabourne, the 83-year-old mother-in-law of the earl's daughter, his 14-year-old grandson Nicholas Knatchbull and 14-year-old Paul Maxwell, from Killynur, Enniskillen in 1979.
Sinn Fein leader Gerry Adams is expected to meet Prince Charles in what would be an historic meeting in Ireland. It is understood that Mr Adams is among guests expected to meet the Prince tomorrow as he begins his four-day tour of Ireland.
The Prince of Wales begins an emotional and historic trip to the west of Ireland where his great uncle Lord Louis Mountbatten was assassinated by the IRA. One of the most poignants stops on the official four day visit to the Republic and Northern Ireland will be on Wednesday when Prince Charles arrives in Mullaghmore, Co Sligo, the site of the atrocity.
All of Ireland's main political leaders have been invited to National University Ireland Galway but the prospect of the visit beginning with the first meeting of a royal and a Sinn Fein leader in the Irish Republic will undoubtedly set the tone.