A total of 16 women have accused the star of films including Se7en and The Shawshank Redemption of behaving inappropriately.
Eight of the women who spoke to CNN said they were victims of harassment or inappropriate behaviour.
Freeman, 80, told Sky News in a statement: “Anyone who knows me or has worked with me knows I am not someone who would intentionally offend or knowingly make anyone feel uneasy.
“I apologise to anyone who felt uncomfortable or disrespected – that was never my intent.”
Eight other women interviewed said they witnessed behaviour they thought inappropriate.
One of the women who claimed she was a victim worked as a production assistant on the set of Going In Style, a bank heist comedy starring Morgan Freeman, Michael Caine and Alan Arkin.
She said what followed was months of harassment at the hands of Freeman, including unwanted touching and comments about her figure.
Among the allegations were claims he repeatedly attempted to lift her skirt.
CNN said the Oscar-winning actor was accused of repeatedly behaving in ways that made women feel uncomfortable on film sets.
Three entertainment reporters told the news channel Freeman made inappropriate remarks during interviews.
One of those was CNN reporter Chloe Melas, who was pregnant at the time and co-wrote the investigation.
She alleged he looked her up and down several times before saying “I wish I was there” and “You are ripe”.
Seven of those who spoke to CNN had worked for Freeman’s production company, Revelations Entertainment, and described an environment of harassment or inappropriate behaviour.
Revelations Entertainment was founded by Freeman in 1996 with Lori McCreary, the current president of the Producers Guild Association.
Freeman won an Oscar for best supporting actor for his role in Million Dollar Baby in 2005 and has been nominated four more times, including as a leading actor in The Shawshank Redemption in 1995 and Driving Miss Daisy in 1989.
He has also been nominated for an Emmy for Revelations Entertainment’s The Story of God with Morgan Freeman.
In 2017, he was honoured with a Screen Actors Guild award for lifetime achievement.