The technology giant and its carrier partners took more than 600,000 pre-order in one day for the new thinner model, the most Apple has ever taken in one day.
Apple said the demand for the iPhone 4 was higher than it anticipated and resulted in approval system malfunctions leaving many customers abandoning the process in frustration.
In a statement Apple says: "We apologise to everyone who encountered difficulties, and hope that they will try again or visit an Apple or carrier store once the iPhone 4 is in stock."
The model, which is 24% thinner than the previous iPhone, includes a 5-megapixel camera with LED flash on the back. Using a front-facing camera, the iPhone 4 will also allow users to see their callers and visa versa.
It will be the first phone to use Apple's iAd mobile advertising network. Apple said it has booked more than $60m worth of advertising already on the network that will be available from 1 July.
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