According to Metro newspaper, AT&T says the iPhone 5 has become the company's fastest-selling iPhone, with customer pre-sale orders over the weekend topping those for previous models.
The new gadget became available for pre-order on 14 September after being revealed a couple of days earlier at an event in San Francisco.
An Apple spokeswoman admitted the demand for the phone officially on sale from 21 September had been overwhelming.
Natalie Kerris said: 'Pre-orders for iPhone 5 have been incredible. We've been completely blown away by the customer response.'
Following the phone being made available for pre-orders, the US company's shares rose and touched a record high, with one analyst calling it 'iPhone 5 fever'.
But due to the massive interest some customers will have to wait two to three weeks for the new device that boasts a slimmer look and a new faster 4G web service.
The company's US website estimated shipments for the iPhone 5 will take two weeks to fulfill.
Apple's website showed buyers in United Kingdom, France and Germany would have to wait as much as three weeks to receive orders when the iPhone 5 started shipping.