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Referring to the assassination off Co Sligo in the Irish Republic, he said he told the royals that he recognised they had lost a relative.
"I said to the Queen and the Duke they too had lost a loved one," he said.
Mr McGuinness revealed some of the detail of the private meeting during a talk show on RTE television.
The killing was discussed briefly after an historic handshake between the pair which has been hailed as a watershed moment in Anglo-Irish relations.
Mr McGuinness has not discussed any of the detail of the meeting until now. When he left the theatre he would only say that the Queen was very nice and that he was still a Republican.
Sinn Fein chief Martin McGuinness told the Queen that he recognised she suffered loss in the Northern Ireland Troubles.
The Stormont Deputy First Minister revealed that he addressed the 1979 IRA murder of her cousin Earl Mountbatten when he met her privately in Belfast last Wednesday.
The former terror commander said the Queen was very gracious about what he said.
Mr McGuinness said he would not detail exactly what he said during the eight minute discussion in the Lyric Theatre, which the Duke of Edinburgh also attended, or how the Queen responded.