U.S. financier Jeffrey Epstein (C) appears in court where he pleaded guilty to two prostitution charges in West Palm Beach, Florida, U.S. July 30, 2008.

The FBI is investigating whether a "criminal enterprise" played a role in the controversial jailhouse death of well-connected sex criminal Jeffrey Epstein, the head of the federal prison system told a Senate committee Tuesday.

But Bureau of Prisons Director Kathleen Hawk Sawyer also testified that there is "no indication, from anything I know," that the wealthy investor's demise on Aug. 10 "was anything other than a suicide."

At the time Epstein died, the former friend of Presidents Donald Trump and Bill Clinton was awaiting trial on child sex trafficking charges.

The FBI did not immediately respond to CNBC's request for comment.

Sawyer's spokeswoman Kristie Breshears later told CNBC that, "When the Director referenced 'criminal enterprise', she was merely mirroring the language Senator [Lindsey] Graham used" in asking Sawyer whether the FBI was eyeing such an enterprise.

"She was referring to looking into possible criminal conduct by staff," Breshears said.

Sawyer's testimony before the Senate Judiciary Committee came on the same day that two guards from a Manhattan jail operated by the BOP were criminally charged with falsifying official records to cover up the fact that they never conducted mandated safety checks on Epstein and other inmates in the hours before he was found unresponsive with a noose around his neck in his cell.

Those guards, Michael Thomas and Tova Noel, allegedly browsed the internet and appeared to have been asleep for about two hours during the time that they were supposed to be making sure that Epstein was alive and accounted for.

Sawyer said Epstein's death is the one incident involving the BOP that has "probably gotten the most public attention."

"This incident was a black eye on the entire Bureau of Prisons," said Sawyer, who became the agency's director less than two weeks after Epstein died.

The New York City medical examiner's office has ruled Epstein's death was a suicide by hanging.

But Dr. Michael Baden, a forensic pathologist hired by Epstein's brother, has said that the injuries found on Epstein's neck were more consistent with those found in homicides.

That view has fueled conspiracy theories about Epstein's death, as have his connections to numerous rich, powerful and high-profile people, such as L Brands' Les Wexner, Microsoft's Bill Gates and Britain's Prince Andrew.

During Tuesday's hearing, one senator underscored to the prisons boss how skeptical many people are about the official ruling that Epstein killed himself.

"Christmas ornaments, drywall and Jerry Epstein. Name three things that don't hang themselves," said Sen. John Kennedy, R-La., flubbing Epstein's first name.

"That's what the American people think. And they deserve some answers," Kennedy said.

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Graham, R-S.C., asked Sawyer about the probes into the incident, which are being conducted by the FBI and the BOP's Office of Inspector General.

"With a case this high profile, there has got to be either a major malfunction of the system or a criminal enterprise afoot to allow this to happen," Graham said.

"So are you looking at both? Is the FBI looking at both?" Graham asked.