(CNN) Former Vice President Joe Biden had a conversation with Anita Hill in which he shared "his regret for what she endured" during the 1991 hearings for Supreme Court Justice Clarence Thomas, his campaign revealed Thursday.

In an interview with the New York Times on Wednesday, Hill declined to call the conversation an apology and said she thinks Biden fails to grasp the damage he did to her and other victims of sexual harassment.

"I cannot be satisfied by simply saying, I'm sorry for what happened to you," she told the Times. "I will be satisfied when I know there is real change and real accountability and real purpose."

Biden oversaw then-Supreme Court nominee Clarence Thomas' confirmation hearings, during which Hill testified that Thomas had sexually harassed her. Biden has faced criticism for years over his handling of Hill's hearing as Senate Judiciary Committee chairman in 1991, when Hill faced intense and probing questioning about her accusations against Thomas from the panel of senators.

When Brianna Keilar asked on "CNN Right Now" whether Biden had privately apologized to Hill, Biden deputy campaign manager Kate Bedingfield replied, "So I'm not going to get into their private discussions, but they have spoken."

When pressed on details, Bedingfield declined to specify when they spoke and whether Biden has apologized, stressing that the conversation was "a private discussion."

A spokesperson for Biden later said in a statement that Biden and Hill "had a private discussion where he shared with her directly his regret for what she endured and his admiration for everything she has done to change the culture around sexual harassment in this country."

Hill has not immediately responded to a CNN request for comment.

Hill told the Times that she could not back Biden until he is held accountable for his 1991 actions and expressed concern over the recent allegations that he has made some women uncomfortable with his behavior

She also echoed her previous calls for a broader apology from Biden, telling the Times, "He needs to give an apology to the other women and to the American public because we know now how deeply disappointed Americans around the country were about what they saw."

Biden said in March that he regrets his actions during the hearings.

"To this day I regret I couldn't come up with a way to get her the kind of hearing she deserved, given the courage she showed by reaching out to us," Biden said at an event in New York . He added that facing "hostile and insulting" questioning, Hill "paid a terrible price -- she was abused through the hearing, she was taken advantage of, her reputation was attacked."

Biden has also said previously that he owes Hill an apology.