Toray Industries Inc., which makes the carbon fiber used in Boeing Co.'s 787 Dreamliner, has agreed to buy Zoltek Companies Inc. for $584 million (about ¥57.6 billion) to expand into markets including windmill blades and auto parts.

Toray, based in Tokyo and the world's largest producer of carbon fiber, will acquire all outstanding shares of Missouri-based Zoltek for $16.75 a share in cash, according to a statement filed Friday with the Tokyo Stock Exchange. The companies plan to complete the deal by early 2014, according to a statement from Zoltek.

Toray said in the statement it wants to expand overseas sales through the acquisition of the U.S. firm, which produces carbon fiber used for windmill blades and automotive parts.

Zoltek, founded in 1975 by Chief Executive Officer Zsolt Rumy, has faced pressure to make changes since March, when activist investor Quinpario Partners LLC bought a 10 percent stake and offered to acquire the company.

Zoltek's shares rose the most in six months after the Nikkei newspaper reported the deal earlier Friday. The shares gained 12.7 percent in New York trading to close at $18.51. JPMorgan Chase & Co. advised Zoltek on the deal.