Microsoft says more than 2 million of its Xbox One consoles have been sold since the system’s launch 18 days ago as the company vies to keep pace with Sony Corp.’s PlayStation 4 during the holiday season.

That works out to an average of 111,111 units per day. And company officials say users have spent over 83 million hours with the games, TV, and apps on Xbox One since the Nov. 22 launch.

Yusuf Mehdi, corporate vice president of strategy and marketing for Xbox, says demand is exceeding supply in the 13 launch markets, with Xbox One sold out at most retailers.

Its makers want the Xbox One to become a user’s main entertainment hub. It supplies a program guide for browsing what’s on TV and what’s highlighted in apps such as Netflix and Amazon. You can listen to music, view photos and make Skype video calls.

The company has “aggressive” plans to restock, said David Dennis, a spokesman for Xbox, in an interview.

“Sales of both platforms are basically on par with each other,” said Colin Sebastian, an analyst at Robert W. Baird & Co. in San Francisco. “Production seems to be roughly the same for both platforms and they’re both doing well at retail.”

Microsoft and Sony are trying to attract gamers against a backdrop of declining console sales. From 2008 to 2012, the market shrank 32 percent to $13.3 billion, according to researcher NPD Group Inc. Both the $499 Xbox One and the $399 PlayStation 4 have more powerful graphics and entertainment applications than older models. To distinguish its machine, Microsoft has been pitching its motion-sensing camera, the ability to control live television and exclusive games like “Ryse: Son of Rome” and “Dead Rising 3.”

“We’re at 2 million at 18 days, and they were at about 2 million at 18 days, so we are running neck and neck,” Dennis said. He declined to provide a forecast for future sales.

Microsoft expects PlayStation 4 sales to top Xbox One when NPD releases its November sales data for the U.S. tomorrow, Dennis said. He attributed the lead to Sony’s extra days on sale in November.

After replenishing initial inventories, Sony and Redmond, Washington-based Microsoft each may sell about 3 million consoles worldwide by the end of the year, according to projections by Sebastian as well as Michael Olson, an analyst at Piper Jaffray Cos. in Minneapolis.

Jack Tretton, president and chief executive officer of Sony’s U.S. computer entertainment division, said Nov. 11 that the Tokyo-based company is confident it can meet analysts’ sales estimates of 3 million units by year-end, and its own target of 5 million units by March. Sony expanded sales of the PlayStation 4 on Nov. 29, and it was available in 32 countries as of Dec. 3.

Both consoles sold more than 1 million units in their first 24 hours in stores.