Gayle King criticized CBS on Thursday for how it had promoted a recent interview that touched on Kobe Bryant, an unusual public rebuke from one of the most powerful figures in the network’s news division.

Ms. King, the lead anchor of “CBS This Morning,” made her frustrations known on Instagram early Thursday in response to a social media backlash over her interview with Lisa Leslie, a former star in the Women’s National Basketball Association and a longtime friend of Mr. Bryant’s.

To promote the five-and-a-half-minute interview, CBS used a 94-second video clip in which Ms. King asked Ms. Leslie about a woman’s 2003 sexual assault accusation against Mr. Bryant, who died last month in a helicopter crash.

“I know that if I had only seen the clip that you saw, I’d be extremely angry with me, too,” Ms. King said in the video she posted on Instagram.

In a statement hours after the anchor’s Instagram post, CBS News said it had mishandled the promotion.

“Gayle conducted a thoughtful, wide-ranging interview with Lisa Leslie about the legacy of Kobe Bryant,” a network spokeswoman said. “An excerpt was posted that did not reflect the nature and tone of the full interview. We are addressing the internal process that led to this, and changes have already been made.”

During the interview, which aired Tuesday on “CBS This Morning,” Ms. Leslie replied to Ms. King’s bringing up the topic by saying that “the media should be more respectful at this time.”

“I just have never seen him being the kind of person that would do something to violate a woman or be aggressive in that way,” Ms. Leslie added. “That’s just not the person that I know.”

The allegation against Mr. Bryant, who reached a private settlement with his accuser out of court after the criminal case against him was dropped, has become a point of contention since his death.

In the social media backlash, the anchor’s critics, who included the basketball star LeBron James, pointed to an excerpt from the interview that appeared on the “CBS This Morning” Twitter account and featured Ms. King and Ms. Leslie speaking solely about the allegation.

In the exchange, Ms. King said to Ms. Leslie at one point, “As his friend, you wouldn’t see it.”

Snoop Dogg was among those critical of Ms. King, saying in an Instagram video, “Why you attacking us?”

“Respect the family and back off,” he added, using obscenities to describe Ms. King. His video had more than one million views. He also posted several pictures of Ms. King, as well as her friend Oprah Winfrey, posing with Harvey Weinstein, the film mogul who has been accused by more than 90 women of sexual misconduct, including rape and harassment.

Ms. King blamed CBS for not providing a fuller picture of the interview in its promotion.

“For the network to take the most salacious part when taken out of context and put it up online — for people who didn’t see the whole interview — is very upsetting to me,” she said in the Instagram video. “And that’s something I’m going to have to deal with them. And there will be a very intense discussion about that.”

The public complaint was unusual: Network anchors usually iron out problems with news executives behind the scenes. Ms. King did not respond to requests for comment through her representatives.

The anchor addressed her online critics weeks after Ms. Winfrey was similarly put under the social media spotlight because of her role as an executive producer on a documentary film focused on sexual assault allegations against the music executive Russell Simmons. Ms. Winfrey ultimately abandoned the project, which went on to be well received by critics at the Sundance Film Festival and has been picked up by HBO Max.

Ms. King is one of the most powerful people at CBS News. Its weekday morning show earns more, by far, than any other program at the network’s news division.

She has become more central to CBS since her former co-anchor Charlie Rose and the CBS chief executive Leslie Moonves were ousted from the network after multiple women accused them of sexual misconduct.

CBS News started a new chapter last year, appointing Susan Zirinsky as the news division’s president, naming Norah O’Donnell as the anchor of “CBS Evening News” and overhauling the morning show, with Ms. King as its centerpiece.