Billionaire financier Carl Icahn (search), the biggest shareholder in Blockbuster Inc. (BBI), Tuesday said the company should put itself up for sale, ratcheting up his proxy battle with the No. 1 U.S. movie renter.

Icahn's statement, in a regulatory filing, is the latest twist in his escalating push for changes at Blockbuster, which is grappling with stiff competition from rivals like online movie renter Netflix Inc. and discount retailer Wal-Mart Stores Inc.(WMT).

A little over a week ago, he accused Blockbuster of being on a "spending spree" with shareholders' money and said he was nominating a slate of three directors, including himself, to the board of the Dallas-based company.

Blockbuster, facing slowing rental demand, is busy pumping money into a new online DVD rental service aimed at battling Netflix and is promoting costly initiatives like the "No Late Fees" campaign to draw customers at its more than 9,000 stores.

On Monday, Icahn's criticism drew a harsh response from Blockbuster, which said Icahn, 69, was creating "turmoil and uncertainty" that could harm the company.

Analysts said a call for Blockbuster to put itself up for sale was just another step to fuel Icahn's proxy fight with the movie renter but won't sway it from focusing on efforts to revive its business.

"If he's realistic, he's going to realize there aren't a lot of buyers out there for Blockbuster. He's just trying to agitate and get Blockbuster to either buy him out or do something to get the share price up," said Dennis McAlpine, an analyst at McAlpine Associates.

Wedbush Morgan Securities Inc. analyst Michael Pachter said if Icahn "sees such amazing value (in Blockbuster) he probably should buy it himself."

He noted that media conglomerate Viacom had tried many times, unsuccessfully, to sell its majority interest in the movie renter before deciding on a split-off.

"The fact is Blockbuster was shopped by Viacom at lower prices and there were no buyers. If in fact there were buyers why did Viacom split the stock at $7?"

A Blockbuster spokesman said the company had told Icahn in a letter that the movie renter made public Monday, that "we are always willing to consider legitimate offers."

But "as you are aware, Viacom considered a number of alternatives for the separation of Blockbuster ... which included extensive discussions ... with numerous financial investors about a potential sale of Blockbuster."

According to regulatory filings, Icahn, through various funds, controls 9.7 percent of Blockbuster's Class A shares and 7.7 percent of its Class B shares.

Blockbuster's A shares were up 19 cents at $10.19 on the New York Stock Exchange (search), where they have risen by almost 7 percent since the start of the year.

On its Web site, Blockbuster has begun mounting a "Vote No on Icahn" campaign for its May 11 annual shareholders meeting.