The exchange, taped Aug. 11, came after Black Lives Matter activists tried unsuccessfully to disrupt one of Mrs. Clinton’s events in Keene, N.H., as they have managed to do at campaign stops by other presidential contenders. Mrs. Clinton agreed to speak privately with the group’s representatives. They have since described her remarks to reporters, but released excerpts from the video for the first time this week. The full conversation was released Wednesday.

Image Protesters performing a “die-in” at Barclays Center in Brooklyn on Aug. 9 for the anniversary of Michael Brown’s death. Credit... Eduardo Munoz/Reuters

In the video, Mrs. Clinton shows little of the soft-edged, convivial but careful persona she often displays at her staged campaign events. She is animated, serious and forceful, jabbing her finger at Mr. Jones, who is from Boston, as if she were arguing with a classmate back at Wellesley. She seems to listen intently, her hands folded in front of her. She concedes that there were unintended negative consequences from her husband’s crime bill, but declines to say there was any racial undertone to that.

Mr. Jones seems to press Mrs. Clinton to bare her soul: “Now that you understand the consequences, what in your heart has changed?” he asks. “How do you actually feel that’s different than you did before?”

Mrs. Clinton calls it a “very thoughtful question” but demurs. “This country has still not recovered from its original sin,” she says, but adds that the “next question” is, “So what do you want me to do about it?”

She urges Mr. Jones to help her come up with a specific “vision and plan.”

“That’s what I’m trying to put together,” Mrs. Clinton says, “in a way that I can explain it, and I can sell it — because in politics, if you can’t explain it and you can’t sell it, it stays on the shelf.”

She shrugs off Mr. Jones’s efforts to elicit a more heartfelt response.

“I don’t believe you change hearts,” Mrs. Clinton says, summarizing her basic view of social policy movements. “I believe you change laws, you change allocation of resources, you change the way systems operate.”