NEW YORK (CNNMoney.com) -- Kirk Kerkorian, already the largest individual shareholder of General Motors, is interested in buying up to 12 million additional shares, or another 2 percent or so, of the world's largest automaker, according to a filing with the Securities and Exchange Commission. GM shares hit a 52-week high on the news

Shares of GM (up $0.51 to $32.79, Charts) jumped more than 4 percent in early trading on the New York Stock Exchange, sending the stock to $33.64. The Dow component stock was trading 1.3 percent higher in early afternoon trade, on higher-than-normal volume.

Kirk Kerkorian said in an SEC filing he wants to increase his stake in GM.

Kerkorian already owns 56 million shares, or about 9.9 percent of GM. His filing says he sent a letter to GM CEO Rick Wagoner saying he is interested in acquiring about 6 million shares of GM common stock and may buy another 6 million shares.

"We are seeking the cooperation and support of the company and its management in connection with these filings and any related proceedings, as we believe additional investment by Tracinda in GM would be viewed positively by investors," Kerkorian said in the letter to Wagoner, referring to his investment firm.

A spokeswoman for GM said it is reviewing the filing.

Kerkorian, who was once the largest shareholder in Chrysler before it was purchased by German automaker DaimlerBenz, has been a critic of GM at numerous times since he started buying shares in early 2005. In June of this year he pushed the company to explore an alliance and cross ownership with Nissan (Charts) and Renault.

The company is nearing the end of three months of talks with those automakers. Wagoner met Wednesday with Carlos Ghosn, the CEO of both Nissan and Renault, and they said the talks would continue at least through mid-October, as originally planned. But many industry observers expect that the negotiations will not produce an alliance.

Kerkorian's filing also did not comment on the reason for his interest in an additional investment in GM, but it again called on GM to move forward with a deal with Nissan and Renault.

"Tracinda continues to believe that a strong opportunity exists in a potential alliance between General Motors, Renault and Nissan and there should be strong General Motors board involvement in the analysis of such a potential alliance, including the utilization of independent advisors," said the statement.

Jerry York, a former Chrysler executive and an advisor to Kerkorian, was named to the GM board earlier this year.

GM spokeswoman Gina Proia said the board has been involved in the review of a potential alliance, and that GM is committed to completing an objective review of a potential deal as originally planned.

GM has made a number of other moves urged by Kerkorian and York in a speech York gave during the auto show in Detroit. Those including cutting its dividend and executive pay as a way to win additional cost cuts from labor.

York had said during that speech in January that Kerkorian would consider upping his stake in GM if he was convinced the automaker was on the right path.

Although GM has been losing market share to Toyota Motors (Charts) and some other import brands, the improved financial outlook has allowed GM to outperform competitors such as Ford Motor (Charts) and DaimlerChrysler (Charts) this year. With a 66 percent gain year-to-date through the close of trading Wednesday, GM was also by far the best performing Dow component.

Kerkorian first made his investment in GM public in May 2005, when he held 22 million shares, for which he paid an average of $26.33.

He made a tender offer at that point for an additional 28 million shares, offering $31 a share, or about a 13 percent premium from where it had closed the day before. But the offer only netted him 18.8 million additional shares, as the price rose above the tender price.

Later that summer Kerkorian purchased 13.1 million additional shares for about $35.28, on average, bringing his total stake to 56 million shares. But as losses at GM climbed, its shares fell, and by the end of the year Kerkorian sold 12 million of his GM shares to take a tax loss against other gains.

He repurchased those 12 million shares in early January for a much lower price than his initial investment. His 56 million shares now have an average purchase price of $30.22.

But Kerkorian's investment in GM has been slipping back and forth between positive and negative return for much of the last several months.

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