A lobbying group for some of the nation’s biggest technology firms is urging new leaders at the Federal Trade Commission to resist growing pressure for changes to the agency’s decades-old antitrust enforcement approach.

The Computer & Communications Industry Association, whose membership includes Alphabet Inc.’s Google, Facebook Inc., and Amazon.com Inc., launched a new initiative this year to counter attacks on the existing U.S. antitrust framework. The group has lobbied Congress on the issue and is now turning its attention to...