The order comes one day after Mr Barr said he was "frankly angry to learn of the MCC's failure to adequately secure this prisoner".
Attorney General William Barr on Monday criticized the detention center.
Attorney General William Barr has expressed outrage that Epstein was able to take his own life Saturday while under the care of the federal Bureau of Prisons while the inmate was facing sex trafficking charges.
Epstein was cleared from suicide watch around July 29 before he was returned to the Special Housing Unit area of the jail.
On the morning of Epstein's death there was shouting and shrieking from his jail cell, a source familiar with the situation told CBS News.
No cause of death has officially been revealed for Epstein, who according to the Manhattan U.S. Attorney was found dead in his cell on August 10 after what was officially called an "apparent suicide". That person also wasn't authorized to disclose information about the investigation and spoke on condition of anonymity.
The union representing federal prison guards, the American Federation of Government Employees Council of Prison Locals, said in a statement after Epstein's death that many guards are forced to work overtime. "Did a BOP employee purposely leave something in the cell that should not have been, and knew given the opportunity Epstein would kill himself?" he wrote.More news: Cincinnati Masters: Andy Murray beaten by Richard Gasquet in singles tennis return
Multiple news outlets have reported that Epstein was left unmonitored for "several" hours before he was found dead of an apparent hanging on Saturday.
New York City's medical examiner has said an autopsy on Epstein was completed on Sunday, but the cause of death remained pending.
A representative for the agency and its acting director, Hugh Hurwitz, were not immediately available to comment.
"Additional actions may be taken as the circumstances warrant", a spokeswoman said. "If no one is watching the screen, then the camera is useless".
Epstein, 66, had been placed on suicide watch - requiring in-person checks every 15 minutes - at the end of July after an incident in which the disgraced financier was discovered semiconscious in his cell with marks on his neck.
Guards in Jeffrey Epstein's unit were working "extreme overtime" in the hours before his death, leaving gaps in his supervision, USA media report.
Some left-wing activists accused the president of endorsing - what they call - conspiracy theories that connect Epstein's alleged suicide to Bill and Hillary Clinton.
"Any co-conspirators should not rest easy".
Catherine Linaweaver, who retired in 2014 after 16 months as the MCC's warden, said some people were overreacting to Epstein's suicide because he was well known.More news: 'Little Women' Trailer: Greta Gerwig's Star-Packed Adaptation Of Classic Novel
The accusers said Epstein's death rendered moot all possible objections to scrapping the agreement.
Mr Epstein was already a registered sex offender after pleading guilty in 2008 to Florida state charges of unlawfully paying a teenage girl for sex.
The FBI raided the island Monday after Epstein died in federal custody over the weekend.
According to NYT, this is part of a larger problem where jails are understaffed with correctional officers, and support staff are often put into these positions with minimal training.
Two of Jeffrey Epstein's victims say his death means the the 2007 plea deal he signed with prosecutors - which continues to protect four alleged accomplices from prosecution - should be scrapped.
They have all strenuously denied the allegations.
Epstein served 13 months of an 18 month prison sentence.
"If someone really wants to commit suicide", Linaweaver said, "they're going to do it". In the federal system, suicides are rarer.More news: Kartik Aaryan presents himself to Sara Ali Khan on her 24th birthday