There is “insufficient evidence” to pursue a prosecution against Sinn Fein leader Gerry Adams in relation to the 1972 murder of Jean McConville, according to reports.
The BBC said it understood that no charges would be brought against Mr Adams unless significant new evidence comes to light.
Meanwhile Mr Adams, who was released from Antrim police station on Sunday night by detectives investigating the abduction and murder of the Belfast mother-of-10, described his arrest as a “sham”.
He also referred to a “credible” death threat made against him after walking free, pending a report to prosecutors, as a risk he was prepared to face in the cause of peace.
But Northern Ireland’s First Minister and Democratic Unionist Party leader Peter Robinson said the real victims were Ms McConville’s family and is arranging a meeting with her son.
Mr Adams told an election rally in Belfast on Monday night: “The sham that I was put through in terms of the total failure of the Police Service of Northern Ireland (PSNI) to present any evidential link between me and that awful event is not the way to go forward.
“It sends entirely the wrong signal to all of those people out there who vote for the future, who in 2014 thought we had got away from that kind of practice.
“While we support the PSNI we will not be diverted from our paths and jobs of building the peace.”
The 65-year-old was set free by police after four days of questioning about the notorious killing of Mrs McConville and other alleged links with the IRA.
The former West Belfast MP has vehemently rejected allegations made by former republican colleagues that he ordered her abduction and death and said the family had suffered grievously.
Mr Adams told CNN’s Christiane Amanpour: “The PSNI visited my home late last night and said that there was a serious threat to my life from what they described as criminals.
“That’s the risk that I and others have to take, and are prepared to take, because the peace process is bigger than us.
“This is why we have to be very steadfast and resolute and patient as well.”
A son of Mrs McConville has said Mr Adams threatened him with a “backlash” if he released the names of those he believed were responsible - a claim the Sinn Fein president later denied.
Michael McConville has said his family’s fight for justice will go on after the Sinn Fein leader was freed, but has maintained he could be shot if he disclosed the identities of suspects to police.
He told 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.”
Mr McConville alleged the historic “threat” was made around the time a report was being drawn up by Northern Ireland’s then police ombudsman, Nuala O’Loan, into claims that his mother was an informer was close to being finalised.
Responding to the allegations, Mr Adams claimed he “never said that”. He added: “I can understand absolutely, given what republicans have done to their family and their mother, I can understand absolutely why the McConville family feel the way that they feel, so let me say that as a matter of record.
“But I am very, very clear - and they may reject this - I have been trying my best to support and help all of the victims, but I have a particular wish to help the victims of the IRA.”
Mr Adams also suggested that the controversy over his suspected role in the killing played into the hands of “negative, sinister elements” who oppose the peace process.
But Mr Robinson, who leads the largest party in the devolved parliament at Stormont and shares power with Sinn Fein, said: “Whilst Gerry Adams and Sinn Fein have been playing the victim, it is important to remember that the real victims are the McConville family. Ten children were left orphaned and have never received justice. This was a horrific and brutal crime.”
The rapturous welcome Mr Adams received in a west Belfast hotel on his first public appearance since his release was in marked contrast to the angry scenes outside the police station as loyalists protested at the decision to free him.
There was disorder in the loyalist Sandy Row area of Belfast, with petrol bombs and stones thrown, though no-one was injured.
Wednesday’s arrest triggered a bitter political row at Stormont, with Sinn Fein accusing an “anti-peace process rump” within the PSNI of orchestrating the detention with the aim of damaging the party ahead of the European and local government elections.
This was angrily rejected by political rivals, whose fury intensified when senior Sinn Fein figures indicated that their support for the police - a critical plank in the peace process - would be “reviewed” if Mr Adams was charged.
Democratic Unionist leader Mr Robinson denounced those remarks as “bully boy” tactics.
Mr Adams questioned the timing of his detention and said police had unnecessarily used “coercive” legislation to detain and quiz him.
But Helen McKendry, Mrs McConville’s daughter, told Channel 4 News: “I want the people who dragged my mother from her home, tortured her, killed her, buried her, I want them brought in a court of law.
Mrs McConville was murdered and secretly buried after she was wrongly accused of passing information to the security forces.