Published Tuesday, 31 July 2012
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Nine people were killed and a number of others seriously injured when three IRA bombs exploded in the Co Londonderry village on 31 July 1972.
In a statement, Mr McGuinness said the deaths and injuries "were wrong".
"All of the deaths and injuries inflicted on totally innocent people in this quiet village 40 years ago should motivate everyone in our society to ensure such terrible tragedies never happen again," the former IRA commander added.
A car bomb exploded outside a pub on the town's Main Street, instantly killing a woman, man and nine-year-old girl, and fatally injuring two others.
The events of that day were appalling and indefensible and they should not have happened.
A second bomb was found in a van close to the post office and, as police cleared the area, people moved towards the Beaufort Hotel, where a third device had been left in a minivan.
The coroner described the attacks as "sheer, unadulterated, cold, calculated, fiendish murder".
In 2010, a Police Ombudsman report found police, church and state colluded to protect Father James Chesney, who was suspected of being involved in the bombings.
The priest was transferred in 1973 to a parish in Co Donegal outside the Northern Ireland jurisdiction and he was never questioned by police.
Fr Chesney died in 1980 in Donegal, and in 2010 it was revealed that Mr McGuinness had visited the priest on his deathbed. But the MP, who had previously denied knowing Fr Chesney, said the Claudy bombs were not mentioned.
It is also 40 years since Catholic teens Daniel Hegarty and Seamus Bradley were shot in Derry by the army during Operation Motorman, which attempted to re-establish a military presence in the Bogside and Creggan areas.