Joel Kjellgren, data center manager, walks in one of the server rooms at the Facebook Data Center, on Nov. 7, 2013 in Lulea, Sweden. Agence France-Presse/Getty Images

WASHINGTON—The U.S. government plans to give up control over the body that manages Internet names and addresses, a move that could bring more international cooperation over management of the Web, but will make some U.S. businesses nervous.

The Commerce Department said Friday it plans to relinquish its oversight of the Internet Corporation for Assigned Names and Numbers, or Icann, which manages a number of technical functions that serve as signposts to help computers locate the correct servers and websites.

The action is viewed as a response to increasing international concern about U.S. control over the Internet's structure, particularly in light of the recent disclosures about surveillance by the NSA and other U.S. intelligence agencies.

Other governments have complained that the department's contract with Icann gives the U.S. unique influence over the Web, which it could use for a wide variety of purposes. In response to those concerns, the Obama administration is convening a process to create a new oversight structure for Icann when the current contract runs out in September 2015.

Alan Marcus, senior director of the World Economic Forum, said "the NSA tarnished the U.S. stewardship" of the Web. Mr. Marcus said the U.S. needs to relinquish control over the Web before new leadership can emerge. "There are real issues that get clouded" by U.S. leadership, he said.

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The action had been debated among technologists and policy makers, but the prospect of the U.S. relinquishing control concerns some businesses because of the potential for censorship.

"If you hand over domain-name registration to someone who doesn't want certain classes of domains registered, then you're setting up a censorship structure," said Bill Reinsch, president of the National Foreign Trade Council, which represents businesses.

In recent years U.S. policy makers have pushed back against calls from nations including China and Russia for the U.N. and ITU to have a greater role in overseeing the structure of the Web. U.S. officials have previously argued that such an arrangement would lead to the repression of free speech and the Balkanization of the Internet.

"We thank the U.S. government for its stewardship, its guidance over the years. We thank them today for trusting the global community to replace this stewardship with the appropriate accountability mechanisms," Icann CEO Fadi Chehadé said.

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Icann will launch the process later later this month at Singapore event and collect input throughout the year, with an aim of having the new governance structure completed by September 2015 when the existing contract with the Commerce Department expires. Anyone with an interest in how the Internet is managed is invited to take part.

According to Larry Strickling, administrator for the Commerce Department's National Telecommunications and Information Administration the new governance model must ensure that Icann is free from government influence. The plan must also fulfill several other conditions, such as preserving the security and stability of the Internet while keeping it open and free from censorship.

Until 1998, the functions were managed by Jon Postel, a computer scientist at the University of Southern California, one of the early pioneers of the World Wide Web. Upon Postel's death in 1998, the Commerce Department issued a contract to Icann to take over those functions, making Icann the primary body in charge of setting policy for Internet domains and addresses.

Mr. Strickling said the U.S. always viewed its role as overseeing Icann as temporary.

"The Internet was built to be borderless and this move toward a more multistakeholder model of governance creates an opportunity to preserve its security, stability and openness," said Vint Cerf, Google vice president and chief Internet evangelist, in a statement.

Some Silicon Valley executives support the move, which they view as inevitable in light of the concerns over the NSA disclosures.

"I'm not sure they have any choice," said Peter Schwartz, senior vice president of global government relations for software maker Salesforce.com Inc., who heard a presentation from Icann Thursday in Silicon Valley. "They're better off getting out ahead of it."

—William Mauldin contributed to this article.

Write to Gautham Nagesh at gautham.nagesh@wsj.com