By Micah Maidenberg

Elliott Management Corp. is pressuring Crown Castle International Corp. to overhaul its approach to its fiber-cable business, which the hedge fund says has weighed on the company's market value despite billions in investment in recent years.

Elliott on Monday publicly released a letter it sent to the Crown board that criticized what it called disappointing returns tied to the $16 billion it has invested to build up the company's fiber-cable business, including a $7.1 billion acquisition three years ago.

Crown's fiber strategy "has not been effective and has significantly detracted from shareholder returns," Elliott said in the letter. The investment firm said it controls an economic interest of $1 billion in the company and has been speaking with Crown executives privately for more than a month.

Crown defended its strategy in a statement Monday and said that it has beaten the S&P 500 index on a total-return basis for one-, three- and five-year periods through July 2.

"While we firmly believe our strategy best positions Crown Castle to deliver near- and long-term value creation, we remain open to having continuing dialogue with Elliott, as we do with all shareholders," Crown said.

Shares of Crown rose 2% in morning trading.

The company, based in Houston, owned, operated or leased about 40,000 wireless towers and 80,000 route miles of fiber as of the end of last year, according to its latest annual report. It rents out wireless capacity on its towers under long-term deals to major wireless carriers, the report says. The fiber business supports so-called smart cells that bolster its towers with added capacity and by helping customers with high-bandwidth data needs.

Elliott, run by Paul Singer, said it doesn't believe that Crown should own the fiber assets, and cited stronger return performance by competitor tower-owners American Tower Corp. and SBA Communications Corp.

"Relative to its close industry peers, Crown Castle has underperformed on a consistent basis for more than a decade," the hedge fund said in the letter.

But the investor said selling the fiber business or spinning it off into a new company would likely be disruptive and cost more than the value created from any such transaction.

Elliott wants Crown to change how it manages the fiber business by focusing on its highest-return opportunities and by incorporating incentives for the unit tied to returns on invested capital.

In addition, Elliott said in the letter that it wants Crown to address its "long-tenured board to improve oversight of its capital allocation approach and ensure Crown Castle's underperforming fiber business has the appropriate management skill set to deliver improved results."

Elliott is well-known for pushing for changes at companies it invests in, including Marathon Petroleum Corp. and Twitter Inc, among others.

Write to Micah Maidenberg at micah.maidenberg@wsj.com