Fortnite still unwelcome in Apple's mobile App Store
The two firms are fighting over whether Apple's tight control of the App Store, and its 30 percent cut of revenue, counts as monopolistic behavior.
US District Court Judge Yvonne Gonzalez Rogers had previously rejected a similar request by Epic, and appeared to remain unmoved at Monday's hearing.
The judge said she didn't expect a trial over the dispute to start until July of next year, at the earliest, given her calendar.
She advised Apple and Epic to request a jury to hear the case and is to issue a written explaining Monday's ruling.
The legal battle comes as Apple puts priority on selling digital content and subscription services to the one billion-plus people around the world using devices powered by its iOS mobile operating software.
Major app developers including Epic and streaming music giant Spotify recently formed a coalition to press for new terms with the major online marketplaces operated by Apple and Google.
Google runs a Play Store for apps tailored for devices powered by its Android software and also takes a commission, but people are free to get apps from other online venues.
The case comes amid rising criticism of the fees and terms imposed by the app stores, and legal challenges by both Epic and Spotify to Apple's commission for online subscriptions.
But Epic did not back down from its fight against Apple, accusing the tech giant of being "a monopolist."