SUN VALLEY, Idaho — Sumner M. Redstone, the chairman and controlling shareholder of Viacom and CBS, is usually a ubiquitous figure here at the investment bank Allen & Company’s annual conference, but even in his absence Mr. Redstone is likely to be the talk of this longtime playground for the well-heeled.

In a CNBC television interview to be shown on Thursday, Mr. Redstone apparently reignited a long-running dispute with his daughter, Shari, over future control of the family media empire as father and daughter challenged each other’s version of events. The New York Times, which has an online relationship with CNBC, was provided a copy of the transcript upon request.

In the interview, Mr. Redstone said flatly that his daughter was no longer the company’s heir apparent and that she would leave the board as part of an agreement he had reached with her.

“Will she succeed you?” David Faber, a CNBC correspondent, asked on the program “Business Nation,” which he moderates. Mr. Redstone replied, “No.”

“The reason she won’t succeed me is not she — that she isn’t qualified,” he added, comparing CBS and Viacom with National Amusements, the movie theater company where his daughter is president. “But I have made it clear that good governance requires — these are two public companies, they’re not private like National — that two companies, the boards should decide who succeeds me. I’m not worried about it ’cause it’s going to be another 20, 30 years.”

Told of Mr. Redstone’s comments, Nancy Sterling, a spokeswoman for Ms. Redstone, said the comments were “absolutely inaccurate.” Ms. Sterling said that “there is no final agreement” and as a result, “this calls into question the veracity of anything else he might say.”

She acknowledged that the father and daughter were in negotiations — which included a confidentiality agreement — and said she was “only speaking because he broke it first.”

In a separate e-mail statement, Ms. Sterling said that Ms. Redstone would not publicly comment on her father’s characterization of the talks.

People close to the negotiations, who declined to be identified because the talks were continuing, said that a deal had been reached in principle to buy out his daughter’s interest in CBS and Viacom. The deal, according to these sources, essentially involves his daughter’s receiving control of National Amusements in exchange for her interest in CBS and Viacom. The two companies control MTV, BET, the Paramount movie studio, Showtime and the CBS broadcast network, among other assets.

The family holding company, National Amusements, holds the family’s stakes in CBS and Viacom, as well as a 1,500-screen movie theater chain. Mr. Redstone, 85, owns 80 percent of National Amusements, while Shari Redstone, 54, owns 20 percent. National, in turn, controls 79 percent of the vote in Viacom, and 76 percent of the vote in CBS. National owns 11 percent of the equity of each media company.

As part of the deal, according to Mr. Redstone’s CNBC interview, Shari Redstone would leave the boards of both CBS and Viacom, effectively ending her hopes of succeeding her father at the helm of the companies.

“I really am doing this to accommodate Shari,” he said in the interview, adding that she “has done a great job running the circuit, operating it.”

Mr. Redstone’s falling out with his daughter, which spilled into public view last summer, is one of several conflicts he has had over the years with executives, family members and even movie stars.

In 1999, at a news conference for Viacom’s purchase of CBS, Mr. Redstone interrupted Mel Karmazin, CBS’s chief executive, by blurting into a microphone, “I’m in control! Remember — I’m in control!”

In 2006, Mr. Redstone settled a lawsuit filed by his son Brent that sought to dissolve the family trusts, by buying out his son’s interests and leaving Ms. Redstone with a 20 percent stake that is valued at some $1.6 billion.

Ms. Redstone was invited to Sun Valley, but canceled for business reasons, according to her representative.

This article has been revised to reflect the following correction:

Correction: July 15, 2008
An article on Thursday about a CNBC television interview with Sumner M. Redstone, the chairman and controlling shareholder of Viacom and CBS, in which he said that his daughter, Shari, was no longer the company’s heir apparent, misidentified the source of the information that a deal had been reached in principle to buy out his daughter’s interest and have her leave the boards of the two companies. That information was provided by people close to the negotiations who declined to be identified because the talks were continuing. Mr. Redstone did not make those points during his interview with David Faber of CNBC.