(CNN) Jill Biden says California Sen. Kamala Harris implied her husband Joe Biden is racist with her attack on the former vice president during the first Democratic presidential debate.

In an exclusive interview with CNN's Chris Cuomo airing on Monday, Jill Biden called Harris' criticism of Biden over race and segregation "the biggest surprise" to her in the party's 2020 race so far -- but said voters "didn't buy it."

Her comments come as Biden and Harris battle to win over black voters, a crucial constituency in the Democratic nominating contest. Biden has pointed to his time as former President Barack Obama's vice president as well as his own legacy on civil rights to defend himself, while Harris has taken aim at elements of Biden's earlier career in the Senate.

In the late-June debate, Harris criticized Biden's comments at a private fundraiser earlier in the month about the "civility" of the Senate during an era in which he worked with segregationists in the chamber. She also lambasted his early-career opposition to federally mandated busing.

"I think that they were looking at the past. I mean, the one thing you cannot say about Joe is that he's a racist. I mean, he got into politics because of his commitment to civil rights. And then to be elected with Barack Obama, and then someone is saying, you know, you're a racist?" she said.

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