“We all know there’s systematic racism in this criminal justice system — there’s no doubt about that,” Ms. Klobuchar responded, before saying she had decreased incarceration of black people during her tenure as prosecutor and diversified the office.

The questioning underscored a source of concern for Ms. Klobuchar, who came in fifth in the Iowa caucuses and is rising in polls of New Hampshire voters, as her presidential campaign begins to look to the more racially diverse states that will vote next.

While former Mayor Pete Buttigieg of South Bend, Ind., has faced more skepticism about his ability to attract black voters, Ms. Klobuchar has similarly low — and in some cases worse — polling numbers among them, particularly in South Carolina.

Ms. Klobuchar cited her victories in Minnesota as evidence that black voters could come to support her.

“My challenge is to get people to know me,” she said, sounding a lot like Mr. Buttigieg. “I’ve always had strong support in my elections at home, and I have a number of key leaders in the African-American community in Minnesota that have gone and campaigned for me.”

Mr. Burrell was convicted in the 2002 shooting of Tyesha Edwards, who was 11 when she was killed by a stray bullet. But The A.P. quoted a co-defendant as saying that he, not Mr. Burrell, was responsible for the shooting.

Ms. Klobuchar oversaw Mr. Burrell’s first trial, conviction and sentencing in 2003. That conviction was later reversed by the Minnesota Supreme Court, which found that a key statement made by Mr. Burrell should not have been used in the trial.