A federal judge ruled on Wednesday that Apple must loosen its grip on its App Store and stop collecting a commission on some app sales, capping a five-year antitrust case brought by Epic Games that aimed to change the power that Apple wields over a large slice of the digital economy.

The judge, Yvonne Gonzalez Rogers of U.S. District Court for the Northern District of California, rebuked Apple for thwarting a previous ruling in the lawsuit and said the company needed to be stopped from further disobeying the court. She criticized Tim Cook, Apple’s chief executive, and accused other executives at the company of lying.

In her earlier ruling, Judge Gonzales Rogers ordered Apple to allow apps to provide users with external links to pay developers directly for services. The apps could then avoid the 30 percent commission that Apple charges in its App Store and potentially charge less for services.

Instead, Judge Gonzalez Rogers said on Wednesday, Apple created a new system that forced apps with external sales to pay a 27 percent commission to the company. Apple also created pop-up screens that discouraged customers from paying elsewhere, telling them that payments outside the App Store may not be secure.

“Apple sought to maintain a revenue stream worth billions in direct defiance of this court’s injunction,” Judge Gonzalez Rogers wrote.

In response, she said Apple could no longer take commissions from sales outside the App Store. She also restricted the company from writing rules that would prevent developers from creating buttons or links to pay outside the store and said it could not create messages to discourage users from making purchases. In addition, Judge Gonzalez Rogers asked the U.S. attorney for the Northern District of California to investigate the company for criminal contempt.