Despite all the technical and server snafus, AT&T has sold out of the company’s allotment of iPhone 4 pre-order units and isn’t taking any more orders. And Apple has bumped its shipping date for the iPhone 4 from June 24 to July 2.

AT&T said in a statement that June 15 “was the busiest online sales day in AT&T history.” That’s when pre-orders for the iPhone 4 began. It also says that “pre-orders for iPhone are temporarily suspended.”

As for Apple’s online store, those buying the new phone is now told Apple will start shipping their examples by July 2. Only the 8GB iPhone 3GS is still due to ship on June 24.

The iPhone 4 is priced at US$199 for the 16GB model, and $299 for the 32GB model, based on a two-year contract. It’s initially available in the U.S., France, Germany, Japan, and the U.K.