McConville was the mother of ten who was abducted by the IRA in Belfast in 1972 and shot dead. Her body was found 31 years later in 2003 by a passer-by on a Co Louth beach.
Speaking at her home in Co Down, Helen McKendry said: “I don’t think Martin McGuinness should be standing. He should be telling the truth to victims’ families, the whole truth.”
Her husband, Seamus McKendry, also criticised the Derry native: “I think the office of President has too much prestige for any Sinn Féiner to be contesting it.”
The McKendrys demonstrated against Sinn Féin President Gerry Adams when he ran as a Dáil candidate in Co Louth during the last general election.
Elsewhere, the family of Tom Oliver who was kidnapped and killed by the IRA in July 1991 has attacked McGuinness over his failure to say that Mr Oliver was murdered.
McGuinness said he would not disagree with the families of Oliver or McConville when they described the deaths as murder, despite failing to admit that were actually murdered.
Oliver was a farmer who was kidnapped and killed by the IRA, who believed he was a Garda informer, a claim staunchly denied by his family.
Yesterday evening the son of Mr Oliver, Eugene Oliver, issued a statement via Independent candidate Sean Gallagher`s campaign team on behalf of the family.
In it Eugene Oliver said he was really upset when he heard Mr McGuinness warn another candidate (Gallagher) on The Frontline to tell the truth.
“What shallow hypocrisy from a man who has dined out on weasel words for most of his career,” the statement said.
Mr Oliver said he wanted Mr McGuinness to “stop hiding behind weasel words” and admit that his father and Mrs McConville were murdered by the IRA, which McGuinness was a leading member of.
The statement went on to say that everyone saw the “empty words” of Mr McGuinness on The Frontline programme when he refused to describe their deaths as murder.
“Even at this late stage, with just days to go to polling, he could not find it in his heart to admit my father, along with other innocent people, were murdered,” Mr Oliver said.
“He was gunned down in cold blood and even twenty years after, at this remove my family are entitled to finally and unequivocally hear the words ‘murder’ uttered from his lips,” the statement adds.