"Even with sales already in excess of 600,000 units, demand continues to exceed supply, as it's clear this is one of the 'gotta-have' products for the holiday season," said Nintendo of America president Reggie Fils-Aime.
"We've shipped retailers several times the amount of hardware the other company was able to deliver for its launch around the same time -- and we still sold out," he added, in a thinly veiled dig at Sony.
Nintendo, which brought to the world the pudgy Italian plumber Mario, is on a quest for industry dominance again with the Wii which launches in Japan on Saturday.
At 249.99 dollars in the US and 25,000 yen (212 dollars) in Japan, the Wii is about half the price of the PS3.
Nintendo created a big buzz last year when it unveiled an innovative new controller for the Wii shaped like a television remote control and engineered with motion sensors and speakers.
By waving or swinging the controller, it can serve as a sword, tennis racket or car steering wheel, with a built-in speaker and rumble feature.
There is also a "Nunchuku" controller which when connected to the main controller resembles the martial arts weapon.
Nintendo has said 400,000 Wii consoles would be available on launch in Japan -- about four times the number of PlayStation 3s Sony managed to ship here.
The Wii's predecessor, the GameCube, failed to recapture the market share once enjoyed by Nintendo's earlier consoles, despite being cheaper than the PlayStation 2 and Microsoft's original Xbox.
Nintendo aims to ship one million Wiis in Japan and four million worldwide by the end of the year, rising to six million globally by March 2007.