The Guardian said its investigation had uncovered allegations from 16 women that the celebrated US illusionist had behaved inappropriately towards them, including some who said they were under 18 at the time.
Three of the women claim Copperfield drugged them before sex.
The US edition of the British-based newspaper and website said it had spoken to more than 100 people, and had examined police and court records to substantiate the story, which it said covered the period from the late 1980s to 2014.
It said the women who made the allegations had met the entertainer through his work, in a career that spanned decades.
Copperfield's lawyers told the outlet he denied any wrongdoing and had "never acted inappropriately with anyone, let alone anyone underage."
The 67-year-old was previously accused of misconduct in 2018, when a woman named Brittney Lewis said he had drugged and sexually assaulted her three decades earlier.
Copperfield denied that claim.
Lewis is part of the 16 women in the Guardian's report.
The Guardian said it had spoken to another woman, who did not wish to be named, who said that the magician had drugged her and a friend before having sex with each of them.
Lawyers told the outlet that Copperfield denied the claims and noted that no complaints had been made against him when the assaults were said to have taken place.
One woman, who was given a pseudonym in the Guardian article, alleged she had first met the magician after one of his shows when she was just 15.
She said over the following years he would call her late at night and send her gifts, such that she now felt she had been "groomed."
When she turned 18, the pair had consensual sex, she told the outlet.
Copperfield's lawyers told the Guardian he and the woman had a legal and consensual relationship that lasted four years.
Copperfield "strongly denies any suggestion of grooming or any other impropriety."
Copperfield has previously faced scrutiny because of an association with indicted sex trafficker Jeffrey Epstein, who died in prison in 2019.
His name was among those included on court documents related to to Epstein that were unsealed in January. However, the inclusion of his name does not indicate that he committed any crime.
"Our client did not know about Epstein's horrific crimes," the Guardian cited Copperfield's lawyers as saying. "Like the rest of the world, he learned about it from the press."
AFP contacted Copperfield's legal representatives, but received no immediate response.
