Shareholder activist Carl Icahn said he is leading a group of Time Warner investors with a $2.2 billion stake that plans to demand the company buy back $20 billion of shares and spin off its cable-TV business. The chief executive of Time Warner, Richard Parsons, agreed to meet with the investors tomorrow, a person familiar with the matter said.

Mr. Icahn, Franklin Mutual Advisers, Jana Partners LP, and SAC Capital Advisors LLC bought stock and options that would give them a 2.6% stake in New York-based Time Warner, the firms said yesterday in a statement.

Shares of Time Warner, the world’s largest media company, have dropped 4.9% this year, prompting the Icahn group to push Mr. Parsons for changes. Mr. Parsons this year announced a $5 billion stock buyback and the first dividend in four years and will sell a stake in the cable unit, the no. 2 American cable operator. Mr. Icahn said he may nominate candidates to the board to speed up changes.

Time Warner “has not moved quickly enough and it has not proposed measures which would enhance values to the degree necessary to realize the inherent value of Time Warner’s well-positioned and unique assets,” Mr. Icahn said in the statement.

Shares of Time Warner, which owns Fortune magazine, Cable News Network, and America Online, rose 26 cents to $18.50 in New York Stock Exchange composite trading. Stock in Walt Disney Company, the no. 2 American broadcasting and entertainment company, has dropped 5.9% this year, Viacom has fallen 4.3%.The Standard & Poor’s 500 Index had gained 1.8%.

“We would of course speak with any interested shareholder of relevant thoughts and perspectives,” a Time Warner spokesman, Ed Adler, said yesterday. “We have informed Icahn that we’d be happy to meet.”

Time Warner’s units would be worth a total of at least $27 a share if they were split up, according to valuations by analysts, including Michael Kupinski at AG Edwards & Sons.

A separation of the cable business from the company’s magazines, Internet, and movie operations and the immediate repurchase of $20 billion in stock would help “eliminate the discount” between Time Warner’s share price and the “inherent value of its unique assets,” Mr. Icahn said in the statement. Mr. Icahn said he and the other investors plan to discuss his plan with other large holders of Time Warner stock.

Separating assets would in part unwind a company that was built over 20 years and includes properties such as Fortune and Time magazines, the Warner Bros. film studio, and Cable News Network.