The new console, which launched in 13 countries, set a record for first-day Xbox sales and is currently sold out at most retailers, Microsoft said in a statement.
Sony said it sold 1 million PS4 units in 24 hours after launching last Friday in just the United States and Canada. The PS4 expands to other regions, including Europe, Australia and South America, from Nov. 29. It then hits Japan in February.
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Microsoft is locked in a console war with Sony this holiday season. The software giant hopes the Xbox One not only entices gamers but attracts a broader consumer base of TV fans and music lovers with its interactive entertainment features and media apps.
"We are working hard to create more Xbox One consoles," said Yusuf Mehdi, corporate vice president of marketing and strategy at Xbox.
Robert W. Baird & Co analyst Colin Sebastian has said he expects shipments of 2.5 million to 3 million units for both the Xbox One and PS4 in the fourth quarter.
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Both the PS4, priced at $399 in the United States, and the Xbox One, with a price tag of $499, offer improved graphics for realistic effects, processors that allow faster game play and a slew of exclusive video games.