His comments came as a leading party figure also declared that it was prepared to enter government with Labour after the next general election.
Speaking at the start of the party’s Árd Fheis, Mr McGuinness apologised to the family of slain Det Gda Seamus Quaid, after a plaque in his honour was removed from Wexford Opera House for the conference.
The garda was shot in October 1980 when he stopped a van at Cleariestown, Co Wexford, while investigating robberies. The van, which contained explosives, was driven by a member of the IRA and the garda was shot.
The son of the murdered garda and former hurling star recently said a decision by Sinn Féin to hold its conference in Wexford was a slap in the face for the family. The family then removed a plaque from the opera house before the conference.
Last night, Mr McGuinness said: “Garda Quaid was an innocent victim. So it’s absolutely appropriate that Republicans should apologise for what happened to him and apologise directly to his family.”
The North’s deputy first minister said he was willing to meet Gda Quaid’s family.
“From our perspective we recognise there was a very long conflict on the island, specifically in the North and people south of the border were also affected by it.
“And I think it’s appropriate that where people lost their lives apologies should be made, apologies have been made and I think they’re heartfelt.”
Earlier, party finance spokesman Pearse Doherty said that Sinn Féin would enter government with left-wing leaning parties, including Labour.
Members at a special Ard Fheis would have to decide this, he told RTÉs Drivetime.
“If I had my way, it would be parties of the left. That includes the Labour party and Green party.”
However, the Donegal South West TD stressed his party would not consider entering any coalition with parties of the right. This included Fianna Fáil, he said.