The cell-phone industry, leery of any attempt to link its products to radiation, sued Berkeley on Monday over a new ordinance requiring consumers to be warned that carrying a switched-on phone in their pockets or bra might exceed federal safety standards.

The ordinance violates free speech by compelling sellers to convey a message they disagree with, and one that is “inaccurate, misleading, and controversial,” said the suit, filed in federal court by CTIA – The Wireless Association.

The trade group successfully used a similar argument against a San Francisco ordinance that would have required cell-phone retailers to tell customers the phones could expose them to dangerous levels of radiation, classified as possibly cancer-causing by the World Health Organization. The city dropped the ordinance in 2013 after a federal appeals court barred its enforcement.

Berkeley’s ordinance, scheduled to take effect July 1, is more limited. It requires sellers to tell customers that the federal government sets radio-frequency radiation exposure guidelines for cell phones, but that a user may be exposed at levels exceeding those guidelines by carrying the device in a pants or shirt pocket or tucked into a bra when it is switched on and connected to a wireless network. “This potential risk is greater for children,” the notice is required to state.

The lawsuit said the instructions falsely imply that the federal guidelines are safety limits. The Federal Communications Commission has stated, based on “overwhelming” scientific authority, that exceeding its radiation-exposure guidelines “does not pose a safety concern,” because the standards are set 50 times lower than the danger levels, CTIA’s lawyers said.

“According to the federal government, no cell-phone model approved for sale in the United States creates a safety concern,” the suit said.

Berkeley officials said they were confident the ordinance would be upheld. Councilman Max Anderson, the measure’s lead sponsor, said the warning language was taken directly from manufacturers’ statements in product manuals. Harvard Law Professor Lawrence Lessig, helped to draft the ordinance and has agreed to defend it without charge.

“I believe Berkeley has a right to assure its residents know of the existing safety recommendations,” Lessig said by e-mail.

Bob Egelko is a San Francisco Chronicle staff writer. E-mail: begelko@sfchronicle.com Twitter: @egelko