Fils-Aime told CNET that 1.2m units of Nintendo hardware sold during the week of Black Friday, which includes Wii U, Wii, 3DS and DS sales.
The Wii U's 400,000 units was nearly matched by the Wii, which sold 300,000 systems during the same week. Meanwhile the 3DS sold 250,000 systems and was beat by the DS, which sold 275,000 units due to Black Friday sales at various retailers.
"Wii U is essentially sold out of retail and we are doing our best to continually replenish stock," Fils-Aime told CNET.
"Retailers are also doing their best to get the product to store shelves. But as soon as product hits retail, they're selling out immediately."
GameStop previously reported that it had an allocation of 500,000 Wii U systems for launch, with over 1.2 million games pre-ordered for the new hardware.
The Wii U, which is available now in North America and November 30 in Europe, comes in a basic and premium bundle.
The basic pack includes a white Wii U console with 8GB of memory, a Wii U GamePad, an AC adapter and an HDMI cable.
The Premium set will offer the system in black with 32GB of memory, a copy of Nintendo Land, Wii U sensor bar, a GamePad charging cradle, stands for the GamePad and console and Nintendo Network Premium membership.
> We have a Wii U... Ask us anything!
> Read Digital Spy's review of 'New Super Mario Bros U'
> Read Digital Spy's review of 'Nintendo Land'
> Wii U hands-on with Nintendo's lineup: 'Mario Bros U', 'Pikmin 3', more
Watch Digital Spy's Wii U hands-on video below: