Motorola faced the mixed blessing of having to apologise after its website was overwhelmed during a “cyber Monday” promotion for its Moto X smartphone.

“We misjudged the overwhelming consumer demand for Moto X, which was far greater than we expected,” Dennis Woodside, its CEO, wrote.

The company was offering the device for $349, compared with its $499 standard price.

Motorola is subsequently offering the device at the discounted price on Wednesday 5 December and Monday 9 December, and is doubling the amount of handsets available, “to help make up for this major inconvenience to shoppers”.

It is also extending a 30 per cent discount offer on accessories to the two days.

Motorola recently extended availability of its Moto Maker smartphone customisation service more widely available across US operators, and is also updating Moto X to support the latest Android 4.4 (KitKat) platform.