Epstein is also accused of paying off possible co-conspirators to "influence" them, U.S. media have reported.
The 66-year-old was awaiting trial in Metropolitan Correctional Center on federal charges that he sexually abused dozens of teenage girls.
"Every single person in the Justice Department - from your Main Justice headquarters staff all the way to the night-shift jailer - knew that this man was a suicide risk, and that his dark secrets couldn't be allowed to die with him", he added.
The attorney general also said he and the whole Department of Justice were appalled and angry to learn about the Metropolitan Correctional Center's failure to adequately secure Epstein.
He added: "We will get to the bottom of what happened and there will be accountability".
Barr vowed that Epstein's co-conspirators will be brought to justice during his Monday remarks.
"In addition to the FBI's investigation, I have consulted with the [DoJ] inspector general who is opening an investigation".
The MCC is operated by the federal Bureau of Prisons, a unit of the Justice Department which Barr heads. (Don Emmert/AFP/Getty Images) Assistant U.S. Attorney Alex Rossmiller (R) speaks as Jeffrey Epstein looks on during a a bail hearing in this court sketch in NY on July 15, 2019. She has not been charged and has denied all allegations of any wrongdoing in this case.
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The incident, which authorities have classified an "apparent suicide", triggered multiple investigations of how such a high-profile inmate, who was supposed to have been carefully monitored, could have died in federal custody. A private pathologist, Michael Baden, who previously served as the city's chief medical examiner, observed the examination at the request of representatives of Epstein, which is routine practice, Sampson said. In a court filing on Monday, two unnamed accusers of Epstein urged a federal judge in West Palm Beach, Florida, to scrap portions of Epstein's 2008 non-prosecution agreement with federal prosecutors there that provided immunity to his alleged co-conspirators from criminal charges.
An attorney for Epstein, Marc Fernich, said jailers failed to protect Epstein and prevent the "calamity" of his death and he had "long since paid his debt to society" for his crimes.
Despite that, Epstein had been taken off suicide watch, a special set of procedures for inmates deemed in danger of taking their own life, a source familiar with the matter told Reuters.
Epstein, who was being held without bail, faced life in prison if he was convicted.
US President Donald Trump has shared two posts about Jeffrey Epstein's death in jail, which allude to links to Bill and Hillary Clinton.
The outcry led Alex Acosta, the then-US labour secretary who as a federal prosecutor helped Epstein negotiate the deal, to resign.
U.S. financier Jeffrey Epstein appears in a photograph taken for the New York State Division of Criminal Justice Services' sex offender registry March 28, 2017 and obtained by Reuters July 10, 2019.
"If someone really wants to commit suicide", Linaweaver said, "they're going to do it".
His death is another black eye for the grim Metropolitan Correctional Center in lower Manhattan, which holds almost 800 inmates awaiting trial in federal court or serving short-term sentences.