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Sinn Féin President Gerry Adams has denied that he made any threats to Michael McConville during their past conversations.
Quoted on the party's website, Mr Adams said: “My sole purpose in meeting with Michael McConville was and is to help the family."
"I can understand the antipathy they feel toward republicans given the abduction and killing of their mother and the life they subsequently had.
"However, I made no threat against Michael McConville and neither did I warn of backlash."
There is "insufficient evidence" to pursue a prosecution against Sinn Fein leader Gerry Adams in relation to the 1972 murder of Jean McConville, reports say.
The BBC said that it understands no charges would be brought against Mr Adams unless significant new evidence comes to light, according to the Press Association.
Gerry Adams has been warned of a "credible" death threat, Sinn Fein said.
The message was passed to the PSNI by Mr Adams' wife while he was not at home.
Mr Adams, was released last night after four days of questioning about the notorious 1972 killing of Jean McConville and other alleged links with the IRA.
The son of murdered Jean McConville has said Gerry Adams threatened him with a "backlash" if he released the names of those he believed were responsible.
Michael McConville has said he along with his family will continue to fight for justice after the Sinn Fein president was freed after questioning, but has maintained he could be shot if he disclosed the identities of suspects to police.
Mr Adams, 65, was released after four days of questioning about the notorious 1972 killing of the mother-of-10 and other alleged links with the IRA, he vehemently rejected the allegations.
Mr McConville told the BBC Radio 4's Today programme: "Gerry Adams says to me 'Michael, you are getting a letter of support from the republican people'. He says 'if you release the names I hope you are ready for the backlash'.
"I took it as a threat."
Northern Ireland should be wary of investigating historic cases of murder which took place during The Troubles as "they are in the past" and the public does not want "to go back to that".
Labour's Peter Hain told Good Morning Britain he did not think digging up the past would bring justice or closure to the victim's families.
"I do not think that going back 40 and more years in this fashion is actually going to take Northern Ireland forward, nor do I think, in the vast majority of unsolved cases, it will bring any sense of justice to victims."
The Government is "confident" authoritative institutions in Northern Ireland, like the police, are independent.
Speaking to Good Morning Britain, the Northern Ireland Secretary dismissed calls from the son of disappeared Jean McConville to have her murder investigated by an independent body.
Theresa Villiers explained: "I am confident that the current institutions in Northern Ireland, the police service of Northern Ireland, and other institutions are independent. They will make fair and balanced decisions on this case, as they do in all others."
Sinn Fein leader Gerry Adams will refocus on election campaigning today as the political fall-out from his release from police custody continues to reverberate around Stormont and beyond.
The republican party is holding an European election rally in Belfast tonight, with a similar event planned in Dublin tomorrow, as Mr Adams resumes the canvassing activities he claims his detention over the 1972 murder of mother-of-10 Jean McConville was designed to thwart.
Sinn Fein leader Gerry Adams was defiant following his release from custody tonight, again rejecting allegations made by former republican colleagues that he ordered the abduction and killing of mother-of-ten Jean McConville.
Despite his criticism of the manner in which he was arrested, he reiterated his support for the PSNI and the peace process.
Sinn Fein leader Gerry Adams said he supports the PSNI, though he criticised the timing and duration of his arrest, and said elements within the police, "the old guard" who are against change, "cannot win".
Latest ITV News reports
Adams attacks reasons for his detention and denies McConville murder
It is claimed IRA volunteers described what happened the night Jean McConville was murdered to Boston College's "Belfast Project".