David Bossie, the former deputy campaign manager for President Trump and a veteran conservative activist, apologized on Sunday after he told a black guest on Fox News, “You’re out of your cotton-picking mind.”

Mr. Bossie made the remark during an on-air discussion on Sunday morning with Joel Payne, a Democratic strategist and frequent Fox guest, who fumed at Mr. Bossie afterward, telling him: “I got some relatives who picked cotton. And I’m not going to sit here and allow you to attack me like that.”

Mr. Bossie’s words prompted a rare on-air repudiation from Ed Henry, the host of the program on which the men appeared, and from the network itself. A Fox News spokeswoman released a statement on Sunday that called Mr. Bossie’s outburst “deeply offensive and wholly inappropriate.”

“His remarks do not reflect the sentiments of Fox News and we do not in any way condone them,” the statement added.