More than 20 women have spoken to the BBC as part of a special investigation, coming forward with allegations of assault and physical violence at properties in London and Paris.
Five women alleged they had been raped by Mr Al Fayed, the broadcaster reported.
Mr Al Fayed, who died in 2023, had previously been accused of sexually assaulting and groping multiple women.
A 2015 police investigation did not lead to any charges.
Harrods' current owners said they are "utterly appalled" by the allegations of abuse perpetrated by the late billionaire, adding: "As a business we failed our employees who were his victims and for this we sincerely apologise."
In July 2023, Harrods began settling claims with women who came forward with allegations of sexual abuse at the hands of Mr Al Fayed.
Rachel, not her real name, told the BBC she was raped after staying at one of Mr Al Fayed's apartments after a late shift at work.
"I made it obvious that I didn't want that to happen. I did not give consent. I just wanted it to be over," she said.
"I remember feeling his body on me, the weight of him. Just hearing him make these noises. And just going somewhere else in my head."
In a statement, Harrods said: "We are utterly appalled by the allegations of abuse perpetrated by Mohamed Al Fayed."
"These were the actions of an individual who was intent on abusing his power wherever he operated and we condemn them in the strongest terms.
"We also acknowledge that during this time as a business we failed our employees who were his victims, and for this we sincerely apologise.
"The Harrods of today is a very different organisation to the one owned and controlled by Al Fayed between 1985 and 2010, it is one that seeks to put the welfare of our employees at the heart of everything we do."
The company said that since new information came to light in 2023 about historic allegations of sexual abuse by Mr Al Fayed, it has been its priority to settle claims in the quickest way possible to avoid lengthy legal proceedings for the women involved.
"While we cannot undo the past, we have been determined to do the right thing as an organisation, driven by the values we hold today, while ensuring that such behaviour can never be repeated in the future," Harrods said.
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