Microsoft has announced that almost 10 million Xbox One consoles have been shipped to retailers, but have not specified how many have been sold to consumers.
The firm also claims to have outsold Sony's PlayStation 4 for the past two weeks in the US.
In a statement on the Xbox News Wire, Xbox corporate vice president of marketing, strategy and business, Yusuf Mehdi said: "Sales have skyrocketed since the new price took effect on 2nd November."
Mehdi is referring to the limited-time price of $350, down from the $400 model without the Kinect motion camera and the $500 launch model with a mandatory Kinect. In September the Xbox One dropped to £329.99 in the UK, £20 less than the Kinect-free SKU that launched in the summer.
In August Sony announced that 10 million PlayStation 4 consoles had been sold having led Microsofts device since their launches last year.
Microsoft still sit behind Sony in the console sales race but with a better Christmas line-up are in a good position to gain some ground.
Microsoft's three big-hitters in Q4 2014 - Sunset Overdrive, Forza Horizon 2 and Halo: The Master Chief Collection – are bigger sales prospects than Sony's offerings. LittleBigPlanet 3 will be released later this month and new racing IP Driveclub has been plagued with server issues since launch.
The recent releases of Sunset Overdrive and Halo will have undoubtedly contributed to the console's improving sales, which Mehdi claims tripled the week after the US price drop.