(Photo credit: Jin Lee/Bloomberg)

Verizon Wireless said Friday that it will allow customers to opt out of having the company's controversial tracking code inserted into their Web traffic.

The company previously offered a way for customers to opt-out of having their data used in its online advertising program. But the company continued to insert a unique code into their Web traffic, angering civil liberties groups who said the technology could be used to track customers movements on the Internet -- even if they took steps to protect their privacy. Now, the company is taking steps to give users more control.

Debi Lewis, a Verizon spokeswoman, issued a statement first reported on by the New York Times about the change:

Verizon takes customer privacy seriously and it is a central consideration as we develop 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.

We listen to our customers and provide them the ability to opt out of our advertising programs. We have begun working to expand the opt-out to include the identifier referred to as the UIDH, and expect that to be available soon. As a reminder, Verizon never shares customer information with third parties as part of our advertising programs.

Verizon began inserting the tracking code into the Web traffic of its "retail customers" -- those not on business or government contracts -- in 2012. But the program reached a higher profile last fall, when many critics and researchers raised concerns about it, dubbing it a "supercookie. The unique string of numbers, which the company calls a UIDH or "Unique Identifier Header," might be used by other companies looking to track users' online behavior or even governments, they worried.  AT&T, which was also experimenting with a program similar to Verizon's,  announced it was dropping the supercookie in November.

But Verizon defended the practice, saying it was "it is unlikely that sites and ad entities will attempt to build customer profiles for online advertising" in a message posted to its Web site. Then earlier this month, privacy researchers revealed that a third-party advertising tracking company was using the code to bring back their own cookies, even if consumers had taken steps to remove them. The company, TURN, has since said it will discontinue the practice.

The civil liberties watchdogs at the Electronic Frontier Foundation recently launched a petition asking the Federal Trade Commission and Federal Communications Commission to investigate Verizon for what the organization believes is "unfair and deceptive" practices related to the tracking code. "The telecom giant did not properly disclose the nature of the tracking header, they do not allow customers to opt-out of the tracking, and their current explanation of its use is deceptive at best," the petition argues.

Members of Congress have also gotten involved, with Sens. Bill Nelson (D-Fla.), Richard Blumenthal (D-Conn.), Brian Schatz (D-Hawaii), and Edward Markey (D-Mass.) sending a letter to Verizon asking it about the supercookies on Thursday night.

But even Verizon's willingness to allow customers to opt-out may not be enough to silence some critics, who argue that the company shouldn't automatically enroll its customers in their online marketing efforts in the first place. "Verizon really shouldn't be doing this in the first place and it should really be opt-in, not opt-out," says Jeffrey Chester, the executive director of the Center for Digital Democracy.