Microsoft, based in Redmond, Wash., said it would take a charge of $1.05 billion to $1.15 billion against earnings in the quarter ended June 30. Consumers know they have a problem if three red flashing lights appear on the console. Gamers on online forums have been referring to the event as “the Red Ring of Death” because the machine then shuts down.

The company declined to explain the nature of the failure, but said that it was not caused by a single problem in the console, which it said contained 1,700 components and 500 million transistors. The company also said there were no health or safety concerns involved. The problem began to appear over the last three to four months, Mr. Bach said, after “significant usage” of the consoles. He said the company has taken steps to correct the problem in new devices.

Microsoft said it would extend the warranty of the game console to three years to customers worldwide. Previously, products sold in the United States were covered by a one-year warranty, while Xbox 360 units sold in Europe had a two-year warranty.

In addition, customers who have had their consoles repaired because of the “three flashing lights” problem will be reimbursed for the cost of the repairs.

Microsoft has succeeded in establishing the Xbox brand against the better known Sony PlayStation and other game machines. The Xbox and its successor, the Xbox 360, was the software maker’s first major foray into hardware. Although sales are small relative to the rest of Microsoft’s revenue, the Xbox has been an important venture for the company and was viewed by many analysts as Microsoft’s attempt to compete with the likes of Sony and Apple for control of electronics and entertainment within homes.