Epic Games founder and Chief Executive Tim Sweeney said Apple's control of its platform had tilted the level playing field.
"The 30% they charge as their app tax, they can make it 50% or 90% or 100%. Under their theory of how these markets are structured, they have every right to do that," he told reporters.
"Epic is not asking any court or regulator to change this 30% to some other number, only to restore competition on IOS," he said, referring to Apple's mobile operating system.
The company also accused Apple of barring rivals from launching their own gaming subscription service on its platform by preventing them from bundling several games together, even though its own Apple Arcade service does that.
Apple said its rules applied equally to all developers and that Epic had violated them.
"In ways a judge has described as deceptive and clandestine, Epic enabled a feature in its app, which was not reviewed or approved by Apple, and they did so with the express intent of violating the App Store guidelines that apply equally to every developer and protect customers," the company said in a statement.
"Their reckless behaviour made pawns of customers, and we look forward to making this clear to the European Commission," it said.
Epic Games' EU complaint got the thumbs up from lawmaker Rasmus Andresen at the European Parliament, which will in coming months seek to reinforce EU tech rules proposed by the Commission to rein in U.S. tech giants.
"We as legislators need to ensure that these platforms who act as gatekeepers in the digital market have to respect a predefined set of rules in order to guarantee fair competition and balanced market powers," he said in a statement.
Apple has been taking small steps in recent months towards changing its practices, including lower fees for some developers and giving them a way to challenge its rulings, both of which have not satisfied the company's critics.
Fortnite is slated to come back to the iPhone at some point in the mobile Safari browser. Epic and Apple in recent weeks have been trading documents and conducting depositions ahead of a scheduled May trial in the Epic lawsuit filed last year.
The Commission, which is investigating Apple's mobile payment system Apple Pay and the App Store, confirmed receipt of the complaint.
"We will assess it based on our standard procedures," a Commission spokeswoman said.
Epic Games has also complained to the UK Competition Appeal Tribunal and to the Australian watchdog.
Big companies such as Microsoft Corp , Spotify and Match Group Inc have also criticised Apple's App Store fees and rules.
(Reporting by Foo Yun Chee Additional reporting by Stephen Nellis and Paresh Dave in San Francisco Editing by Barbara Lewis, Kirsten Donovan) ((firstname.lastname@example.org; +32 2 287 6844; Reuters Messaging: email@example.com))