Sprint is suing AT&T for what it calls a "deceptive 5G E campaign" in which AT&T seeks to "mislead customers into believing that it currently offers a coveted and highly anticipated fifth-generation wireless network, known as 5G."

The complaint is a step toward legal standard in the burgeoning 5G space, and could trigger an embarrassing rollback for AT&T in its marketing if the judge rules in Sprint's favor. Tech news site Engadget first reported the lawsuit.

According to the lawsuit:

The significance of AT&T's deception cannot be overstated. Following years of tremendous growth in both the number of data users and in the amount of data being consumed, consumers are now demanding wireless service with faster speeds, lower latency (i.e., faster connectivity), and greater capacity (i.e., the ability to accommodate more users) than current 4G LTE wireless service can deliver. ... By making the false claim that it is offering a 5G wireless network where it offers only a 4G LTE Advanced network, AT&T is attempting to secure an unfair advantage in the saturated wireless market.

The complaint, filed Thursday in the U.S. District Court of the Southern District of New York, seeks to stop AT&T from using the terms "5GE," "5G E," or "5G Evolution," or any designation containing "5G" for its current wireless network offerings. It also includes the possibility that AT&T could pay out damages of an amount to be determined by the court.

"We feel very comfortable with how we've characterized the new service that we're launching," AT&T CEO Randall Stephenson told CNBC's "Squawk Box" Friday. "We've obviously done our homework. We've done a lot of work around how we characterize this and we're being very clear with our customers that this is an evolutionary step."

All four major U.S. wireless carriers have been rushing to claim the first 5G network in the U.S., which has caused confusion for customers. Some of this had led to carriers like AT&T using 5G marketing in areas where 5G will eventually be available, but isn't yet.

"I fully understand why our competitors might be upset with this," Stephenson said. "It's not a play everybody can run. It's a play that we really like, and it's a play that's going to differentiate us in the marketplace as we begin to roll this out over the course of this year."

Some AT&T phones now show a "5G E" indicator where they used to say LTE, for example. This means a customer is in a 5G Evolution market where AT&T has deployed network technology that has peak theoretical speeds of 400 megabits per second, or what AT&T considers the foundation for 5G. But this doesn't mean the customer is actually connected to a 5G network. In fact, customers can't even buy true 5G phones yet.

5G Evolution isn't the same as 5G+, which is what AT&T has named the faster lower-band 5G "mmWave" network. That's the network that will compete with offerings from Verizon, Sprint and T-Mobile, and it's only available in a dozen markets in the U.S. right now.

"The reality is that this network isn't 'new' and '5G E' is a false and misleading term," a spokesperson for Sprint said in a statement. "AT&T is just like Sprint and all the other major wireless carriers currently operating a nationwide 4G LTE network."

AT&T tried to clear up this confusion in a statement to CNBC Wednesday, but it doesn't address why AT&T is suggesting there's actual 5G available when there is not.

"We've brought the '5G E' indicator to some of our most popular and capable smartphones simply to help customers know when they are in an area where the enhanced wireless experience may be available," a spokesperson said. "Customers with a 5G capable device will see a '5G+' indicator when in our mmWave spectrum area. Later this year we'll offer 5G over low-band spectrum, and customers with a capable device will see '5G' in those areas."

The company said in a statement Friday it's been upfront about 5G Evolution as a step toward "standards-based 5G."

"We will fight this lawsuit while continuing to deploy 5G Evolution in addition to standards-based mobile 5G. Customers want and deserve to know when they are getting better speeds," a spokesperson for AT&T said. "Sprint will have to reconcile its arguments to the FCC that it cannot deploy a widespread 5G network without T-Mobile while simultaneously claiming in this suit to be launching 'legitimate 5G technology imminently.'"

When asked for comment, Verizon pointed CNBC to a tweet by Verizon spokesperson Jeffrey Nelson. "5Ge. It's pretend, it's fake, it's the kind of BS that gives marketers, communicators businesses and the wireless industry a black eye," Nelson said.

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Read the full lawsuit: