AT&T blamed yesterday’s iPhone 4 pre-order problems on unexpectedly high demand for the device, citing over 13 million visits to the company’s website.

“iPhone 4 pre-order sales yesterday were 10 times higher than the first day of pre-ordering for the iPhone 3G S last year,” the carrier said in a statement.

While yesterday’s initial rush to pre-order the iPhone 4 crashed AT&T’s ordering system, Apple was still able to sell out of the new smartphone. In its statement, AT&T confirmed a July 2 ship date, as opposed to the earlier arrival date of June 24. Apple reported an arrival date on the backorders of July 6-8.

Many were wondering how Apple was able to sell out of the new iPhone, as AT&T’s website was unable to process orders for most of yesterday. PC World, citing a source close to the carrier, is now reporting that AT&T had not tested the system it was using to process the orders prior to launch of the device.

Apple also released a statement today, apologizing for the problems. Apple said that together with its carrier partners, there were a total of more than 600,000 pre-orders for the new iPhone. “It was the largest number of pre-orders Apple has ever taken in a single day and was far higher than we anticipated, resulting in many order and approval system malfunctions,” Apple said. The company acknowledged that “many customers were turned away or abandoned the process in frustration.”

In-store pick-up reservations for June 24 also have closed. The only option left for those hoping to get the phone before early July is to wait in line at a retail outlet on launch day.

The new iPhone 4, which was unveiled by Apple CEO Steve Jobs at the opening keynote for the company’s Worldwide Developer Conference, is available in both 16GB ($199) and 32GB ($299) models. The phone comes in both black and white, but only black was available for pre-order.