Financier Carl Icahn reportedly intends to push Time Warner to sell off its cable and publishing units.

NEW YORK (CNN/Money) - Billionaire investor Carl Icahn urged Time Warner Inc. to separate its cable business and buy back at least $20 billion worth of its stock on Monday, saying management has not done enough for shareholders.

Icahn -- who along with several hedge funds owns over 120 million shares of Time Warner (up $0.23 to $18.47, Research) -- said he plans to meet this week with Time Warner Chief Executive Richard Parsons to discuss his views of the media company.

While Icahn said that management has done "a commendable job managing each of their various businesses," he criticized it for having "not proposed measures which would enhance values" for shareholders.

A spokesman for Time Warner said the company would meet with Icahn.

"Our board and our management are committed to creating long-term value for all shareholders and we've been on a course that demonstrates that commitment," the spokesman said. "We would, of course, speak with any interested shareholders who have relevant thoughts or perspectives and in that context we have informed Mr. Icahn that we would be happy to meet with him."

Parsons has already started some of the steps that Icahn is pushing for, according to a report published Monday by the Financial Times. Time Warner has announced a $5 billion share buyback plan and said it would spin off about 20 percent of its Time Warner cable business when its acquisition of the Adelphia cable operator is completed next year.

The report said Icahn told Parsons in a call last Friday that he and three other hedge fund investors -- Franklin Mutual, Jana Partners and SAC Capital -- had accumulated a $2.2 billion stake in Time Warner, the biggest media company in the world.

Icahn made his name as a corporate raider in the 1980s and last year set up a $1.6 billion hedge fund that is now used to take stakes and pressure for changes at companies, the paper said.

Time Warner is the parent company of CNN/Money.

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-- from staff and wire reports