AT&T Inc., the largest U.S. phone company, has sued rival Verizon Wireless, saying its advertising about network coverage is misleading.

Verizon’s ads use large areas of white space in maps of 3G network coverage areas to indicate that AT&T customers are “out of touch” in vast parts of the U.S., according to the complaint filed in federal court in Atlanta.

“Contrary to the misleading message conveyed in Verizon’s advertisements, AT&T customers can fully use their wireless devices outside of a 3G coverage area and undisputedly have coverage in areas depicted by the white or blank spaces,” AT&T’s Mobility unit said today in the court document.

AT&T, based in Dallas, is seeking a court order to stop Verizon from using the maps in its ads. Verizon Wireless is jointly owned by Verizon Communications Inc. and Vodafone Group Plc.

“These ads are serving to inform customers where the coverage critical to operating a smart phone is available,” Verizon Wireless spokesman Jim Gerace said in an e-mail. “Considering their limited 3G coverage, our competitor should examine whether they are misleading customers with their fastest 3G network claim.”

Verizon surpassed AT&T as the largest mobile carrier in the U.S. this year after it acquired Alltel Corp. The two companies are competing for a dwindling supply of new customers as there are enough wireless devices to cover about 90 percent of the U.S. population, according to the CTIA wireless industry association.