Discover, through its Pulse Network LLC unit, alleges that "in order to maintain its monopoly, Visa has undertaken a series of illegal actions that undermine competition - harming rival debit networks, merchants, acquirers, card issuers, and consumers."

Representatives at Visa could not immediately be reached for comment outside regular business hours.

Pulse requires its debit cardholders to authorize transactions with a personal identification number (PIN). Most Visa transactions use customer signature.

The lawsuit alleges that "Visa has a long history of making sure that PIN debit does not predominate, including undertaking illegal behavior to fend off competitive threats to its debit network services monopoly."

In the petition, Discover said that Visa is offering economic incentives to merchants to choose the Visa network for transactions.

Discover is challenging a Visa rule that requires financial issuers of Visa signature debit cards to also include Visa's PIN services instead of allowing other PIN networks like Pulse to compete for that business.

The case is Pulse Network LLC v. Visa Inc in the U.S. District Court of Southern District of Texas, Houston Division. Case: 4:14-cv-03391.