The IRA's secret killing and burying of victims accused of passing information to the British security services during the Northern Ireland conflict was cruel and unjustified, Martin McGuinness said.
The senior Sinn Fein member appealed for anybody with information about undiscovered remains of the Disappeared to give it to somebody in authority.
Jean McConville, a widowed mother-of-10, was among 17 people abducted, killed and secretly buried by republican paramilitaries during the Troubles. Members of the IRA claimed some of the victims had "informed" on their activities to the authorities.
Mr McGuinness said: "What happened to those families was totally and absolutely wrong. I believe it was cruel, I believe it was unjustified. Of course the IRA were responsible."
Mrs McConville, a widow, was killed after she went to the aid of a fatally wounded British soldier outside her home in west Belfast's Divis flats. The IRA claimed she was an informer.
Her remains were finally found at Shelling Hill beach in County Louth in the Irish Republic in August 2003.
Ms McConville's IRA killers tried to silence her son days after she vanished, it has been revealed.
Michael McConville, who was 11 when his mother was snatched from her west Belfast home in 1972, was abducted, beaten and threatened at gunpoint by young republicans intent on keeping her disappearance quiet.
Even though a former IRA boss claimed Gerry Adams ordered her murder, the Sinn Fein president again insisted in a special television documentary that he had nothing to do with the young mother's death.
Mr McGuinness told MLAs at a meeting of the Stormont Assembly: "I and other republican leaders have over the course of a number of years been involved in exhorting anyone with any scrap of information whatsover about the location of these bodies to bring them forward and that has brought considerable success for some families but sadly not for other, and I would reiterate my appeal to anyone out there in the community who was in any way involved in any of these situations to bring forward that information.
"It has been a terrible ordeal, it has been a despicable ordeal and I believe there is a huge responsibility on everybody, including myself as a republican leader, to appeal to anybody out there who can assist these families out of the nightmare that they face on a daily basis."