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.
(Read more: Analyst slams new Xbox One)
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.