Former Vice President Joseph R. Biden Jr. on Tuesday acknowledged his role in the Anita Hill hearing, publicly reckoning with a moment from his past that has drawn criticism as he considers a third presidential campaign.

In an emotional speech, Mr. Biden said he recognized the part he played in the aggressive questioning that Ms. Hill faced during the 1991 Supreme Court confirmation hearing for Justice Clarence Thomas, when she testified that Justice Thomas had sexually harassed her.

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“She faced a committee that didn’t fully understand what the hell this was all about. To this day, I regret I couldn’t give her the kind of hearing she deserved,” he said, at an event in New York City honoring students who helped fight sexual violence on college campuses. “I wish I could have done something.”