Published Monday, 21 April 2014
Mr McGuinness was speaking during an Easter Rising commemoration. (© Pacemaker)
The Sinn Féin MLA made the comments in Monaghan as part of the Irish state's commemoration of the 1916 Easter Rising.
Mr McGuinness said that "shared hurts need to be acknowledged, lessened, and if possible healed".
His remarks come after he and several senior members of his party met with the Queen as part of the first Irish state visit to Britain.
The MLA for Mid Ulster said: "Republicans are committed to a genuine process of national reconciliation and this means reaching out to the unionist community in a spirit of generosity and understanding.
"Earlier this month a confident and united Sinn Féin leadership decided that republican representatives, including myself, should participate fully in the Irish President's state visit to Britain.
"Our party leadership took this decision in the context of republican objectives, and as an initiative to further strengthen the process of change and reconciliation.
"Republicans have shown in words and deeds that we are absolutely committed to this process of reconciliation.
"But unionists must also participate in this process.
"They need to reach out to republicans. The conflict was long and bitter. Many people were hurt on all sides.
"No one has a monopoly on suffering."
He added: "It is time to begin discussing how shared hurts can be acknowledged, lessened and, if possible, healed.
"Republicans fully acknowledge the hurt that we inflicted in the course of the conflict.
"Unionists also need to recognise the hurt they have created.
"They need to turn their back on the inequality and repression that marked 50 years of one party rule in the north.
"They need to challenge rejectionist unionists. They need to show positive leadership."
© UTV News