U.S. officials announced plans Friday to relinquish federal government control over the administration of the Internet, a move that pleased international critics but alarmed some business leaders and others who rely on the smooth functioning of the Web.

Pressure to let go of the final vestiges of U.S. authority over the system of Web addresses and domain names that organize the Internet has been building for more than a decade and was supercharged by the backlash last year to revelations about National Security Agency surveillance.

The change would end the long-running contract between the Commerce Department and the Internet Corporation for Assigned Names and Numbers (ICANN), a California-based nonprofit group. That contract is set to expire next year but could be extended if the transition plan is not complete.

“We look forward to ICANN convening stakeholders across the global Internet community to craft an appropriate transition plan,” Lawrence E. Strickling, assistant secretary of commerce for communications and information, said in a statement.