Billionaire investor Carl Icahn has cut his stake in Blockbuster, selling more than 13 million shares of the video rental chain whose woes include the possibility of bankruptcy.

Over the past week, Icahn, who was Blockbuster's largest shareholder according to Thomson One Financial, trimmed his ownership of the Class A shares to 5.1 percent as of March 29, according to a federal filing. In January he reported a 16.9 percent stake.

He also reduced his stake in the company's Class B shares.

The relatively long-term relationship between Blockbuster and Icahn – who has a reputation for buying into a company and spurring management to make changes — goes back to at least 2004, when he spent $83.8 million to buying 5.8 percent of Blockbuster's Class A stock.

At one point he served on the company's board to publicly criticize then-Chief Executive John Antioco publicly.

Blockbuster said on Monday it was not in compliance with New York Stock Exchange minimum market value requirements, which requires listed companies to have a global market capitalization of at least $75 million over a 30-day trading period.

The company, which faces a debt load of nearly $1 billion, said earlier this month that it might need to file for bankruptcy protection.

Blockbuster shares closed on Tuesday at 25 cents a share, and have declined by about 58 percent so far this year.