The former IRA commander addressed an audience in Warrington on Wednesday evening, in a centre built by the peace foundation established in memory of Tim Parry and Johnathan Ball.
Tim, aged 12, and three-year-old Johnathan died when IRA bombs planted in bins devastated the main shopping area of the English town, without warning, on a Saturday afternoon in March 1993.
"There can be no greater tragedy in life than parents having to bury their child," Mr McGuinness said during his speech.
"The deaths of children as a result of the conflict is something that those of us who were engaged in armed organisations, be they British or Irish, have to accept responsibility for."
The Sinn Féin politician, now deputy First Minister of Northern Ireland, was invited to give the annual keynote lecture by Tim's father Colin Parry in what is the 20th anniversary year of the atrocity.
I was once in the IRA. I am now a peace builder. I don't expect anyone to take me at my word. I expect them to take me by my deeds.
"I think it's entirely appropriate that a peace organisation like ours listens to what he has to say," Mr Parry told UTV ahead of the event.
"It doesn't mean I approve of his past in any way, shape or form. I obviously don't and he would know that. He is part of a partnership government which is attempting to bring Northern Ireland into an entirely peaceful situation.
"Of that, I approve."
But a protest was held outside the venue by a victims' group campaigning for justice for the 21 victims of IRA bomb attacks on two pubs in Birmingham in November 1974.
In a statement, the group called for answers about those responsible for the attacks and added: "Once again, ignored victims of terrorism from our community will be standing on the streets while one of the parties responsible for their misery are inside."
Inside the venue, Martin McGuinness continued his lecture by stating that there could be no excuse for the human loss caused by the IRA bomb in Warrington.
"As a republican leader, it would be hypocritical of me to seek to distance myself from the consequences of armed struggle or the IRA's role in it," he said.
He also revealed that, on the day of the attack, he and party colleague Gerry Kelly were due to hold secret talks with a British government representative. The meeting was cancelled, but went ahead two days later.
"The British government could have walked away, but they knew - as we did - that the only resolution to the conflict lay in dialogue," Mr McGuinness said.
Mr Parry had previously met with Mr McGuinness on a number of occasions, even interviewing him for a documentary - which was when he made the snap decision to invite him to give the lecture.
We can't be partisan and decide who we will and won't speak to - it wouldn't work. It would destroy our credibility.
In his address, Mr McGuinness described his meetings with the Parry family as "a significant act of generosity" on their part.
"It has had a lasting impact on me. Gestures like this, though difficult for those bereaved, are crucial to building peace and reconciliation," he said.
"Some families - and the Parry and Ball families are an example of this - turn their tragedy into a worthy and personal crusade for the greater good of humanity."
Ahead of the event, Mr Parry had recognised that his choice of speaker could be seen as controversial, perhaps even more so in Northern Ireland than in England.
"People in Northern Ireland have lived with this awful tragedy for more than 30 years. Feelings run very deep. I understand that and I'm not in any way disrespecting that," he said.
"But nonetheless, what we set up is a peace foundation in memory of our son and Johnathan Ball. The fundamental philosophy behind that is that we will pursue peace building and reconciliation.
"We will actively do that. And for that reason, this approach to Martin is consistent with that approach we've adopted."
Mr Parry added: "I don't attempt to teach anybody lessons. The worst thing I could ever do is get on my high horse and say what I do is a model for everybody."
Regrettably, the past cannot be changed or undone. Neither can the suffering, the hurt or the violence of the conflict be disowned by republicans or any other party to the conflict.
Relatives of the two young victims received apologies from the IRA in the wake of the atrocity, but Mr Parry says that did not make the slightest bit of difference.
"No apology could ever eradicate the pain and the suffering we experienced in the loss of a much loved son. Apologies are meaningless and I take no account of those," he said.
"I simply approach the business of our charity on a pragmatic basis, that we have to make serious and significant steps if we are to be a serious player in this business of peace-building."
Speaking in the Warrington peace centre, Martin McGuinness also touched on another such centre - the proposed facility at the former Maze prison site outside Lisburn, currently on ice.
"It beggars belief that we cannot agree on the building of a peace centre," he said.
"But what is it that has tripped us up? What has tripped us up is the past, how we speak about it, how we present it and how we address it. And its role in reconciliation."
Claiming that unionist fears that it would become a shrine to terrorism had been exploited, Mr McGuinness added: "The exploitation of this fear has only been possible because of our collective failure to address the past.
"And in hindsight, we should have known better."
Republicans cannot make agreements with ourselves. We need unionist partners.
According to Mr Parry, his work in establishing the Tim Parry Johnathan Ball Foundation for Peace - which has become an internationally recognised centre for conflict resolution and victim support - has kept him sane over the years and held his family together.
"It's not in my nature to do nothing," he said.
"I think the foundation and the peace centre we've built have been my road to some kind of redemption and, in light of that, my family have stuck together as well.
"I know for a fact, if this wasn't the road we'd gone down, the implications for my family would have been extreme beyond even losing one child."
Mr Parry now hopes that his organisation can also play a part in the Haass talks, given its work over the years with groups and individuals from Northern Ireland.