Verizon Wireless customers now have the ability to completely opt out of the phone carrier’s controversial ad-targeting program that tagged users with undeletable tracking codes, which critics called “supercookies.”

The company announced in January that it planned to provide a complete opt-out of the program. Verizon said Tuesday that its systems have now been changed to stop inserting the unique identifier, referred to as a UIDH, for customers who don’t want to be in the program.

In the past, Verizon allowed users to unsubscribe from the marketing side of the program, but they had no option to disable being tagged with the customer codes. Some security researchers quickly illustrated that third parties, like advertisers, could easily exploit Verizon’s persistent tracking to continually follow a user’s web browsing activities.

In a statement, Debra Lewis, a Verizon spokeswoman, said privacy is a “central consideration” for the company when it develops new products and services.

“As the mobile advertising ecosystem evolves, and our advertising business grows, delivering solutions with best-in-class privacy protections remains our focus,” Ms. Lewis said. “As a reminder, we never share information with third parties that identifies our customers as part of our advertising programs.”

To disable the header tracking, users can opt out of the program called Relevant Mobile Advertising. When that happens, Verizon stops inserting the header, according to the company. Users can unsubscribe from the program on Verizon’s website or by calling 1-866-211-0874.

In January, four Democratic members of the Senate’s powerful Committee on Commerce, Science and Transportation sent a letter to Verizon’s chief executive, Lowell C. McAdam, demanding an explanation for the company’s data security and privacy practices. Shortly after, Verizon said it would provide a complete opt-out.

But privacy advocates continue to press Verizon. Jacob Hoffman-Andrews, a technologist for the Electronic Frontier Foundation, encouraged Verizon to go a step further.

“This is an improvement, but it doesn’t do nearly enough,” he said. “Verizon should discontinue its header injection program, or at a minimum make it opt-in.”

Verizon’s Ms. Lewis said customers may log in to their accounts to change their participation in the company’s data collection programs — whether it’s opt-in or opt-out — in the privacy section of the company’s website.