Epic made its proposal in a court filing on Thursday to US District Judge James Donato in San Francisco, seeking among other things to require Google Play Store to allow the distribution of competing third-party app stores for six years and limit the company's ability to make agreements with device makers to restrict preloading of competing app stores.
Donato presided over a blockbuster antitrust trial that ended in a jury verdict against Alphabet-owned Google in December.
Representatives from Google and Epic did not immediately respond to requests for comment.
Donato is not bound to grant Epic's proposal, and a hard fight is likely before any permanent order on Google is issued.
But the new filing sets up the next key test of Google's ability to impose controls on app developers and consumers.
Google has defended its app store practices and denied any wrongdoing. (Paul Braven/AAP PHOTOS)
The jury in December said Google unlawfully impeded developers' ability to freely distribute their apps outside of Google's Play Store and kept an overly tight grip on payments for transactions within apps.
Epic's proposed injunction also said Google should be barred from restricting "the ways an app can inform users about out-of-app purchasing options".
Google has defended its app store practices and denied any wrongdoing.
The company has a May 3 deadline to respond to Epic's proposal.
Epic's lawsuit did not demand monetary damages.
North Carolina-based Epic Games is a privately held company, in which China's Tencent owns a 40 per cent stake and Walt Disney about nine per cent as of February.
Google separately in December agreed to pay $US700 million ($A1.1 billion) to resolve state and consumer allegations over its Play Store restrictions.
The company said then it was expanding the ability of app and game developers to provide consumers an alternative billing option for in-app purchases.
Google said it had piloted "choice billing" in the US for more than a year.
Google has said it will appeal the December antitrust jury verdict, and it can separately challenge any reforms ordered by Donato, which could stretch the case for years.
A similar case Epic lodged against Apple in 2020 challenging its grip on its App Store is still being fought after a non-jury trial and appeals.
