William Smith, former chief counsel for the Senate Judiciary Committee, which is led by Sessions, said that in 20 years working with the Republican senator from Alabama, he had seen no evidence of racism.
"Because you are the one black guy that he hired on the committee doesn't make him a civil rights leader, William," Rye told Smith, speaking on CNN's "AC360."
"It actually really doesn't. It makes, it makes, I am not going to. I am going to leave it at that," said Rye, seeming to cut herself off.
But Smith, who repeatedly said Rye was ignorant of Sessions' policies, was not satisfied with Rye's comment.
"You can leave it at that because you have nothing," he shot back.
The exchange, moderated by CNN's Anderson Cooper, had become heated when Rye said Sessions' policies offered a clue to his views on race.
"I don't know if Jeff Sessions is a racist," she said. "I don't know if he is a bigot. I gave you the fruit. I know one thing. We know a tree by the fruit it bears."
In 1986, when Sessions was nominated to be a federal judge, a former Justice Department employee testified that Sessions had made racist remarks. Sessions denied those allegations, but they cost him the judgeship.
On Tuesday, Sessions spokeswoman Sarah Isgur Flores told CNN in a statement the senator "has dedicated his career to upholding the rule of law, ensuring public safety and prosecuting government corruption."
"Many African-American leaders who've known him for decades attest to this and have welcomed his nomination to be the next attorney general," she added. "These false portrayals of Sen. Sessions will fail as tired, recycled, hyperbolic charges that have been thoroughly rebuked and discredited."