In a statement, Brad Smith, the president of Microsoft, said the company welcomed the “opportunity to present our case in federal court.”

Bobby Kotick, the chief executive of Activision, said in a note to employees that the company welcomed the news because it “accelerates the legal process.” He added: “We will now have the opportunity to more quickly present the facts about our merger.”

If Microsoft ushers the deal through, it would be a monumental moment for the $184 billion gaming industry. Microsoft earns billions of dollars each year in the video game business, but competitors like Nintendo and Sony — which makes the PlayStation console — have long been considered to have a better catalog of games that attract players to their devices. Adding Activision and its slate of gaming studios to Microsoft’s Xbox consoles and its games subscription service could even the playing field.

Lina Khan, the F.T.C. chair, has made blocking corporate deals a cornerstone of her strategy to rein in the tech giants and other big companies. The chip maker Nvidia and the defense contractor Lockheed Martin have dropped proposed deals after they were challenged by the F.T.C. under Ms. Khan.

Attempts to block other deals have been less successful. Last year, the F.T.C. tried to stop Meta from buying Within, a start-up that makes a virtual reality fitness game. A federal judge declined to stop the deal from closing, and the F.T.C. dropped its broader challenge to the purchase.