"Demand for the new iPhones exceeds the initial pre-order supply and while a significant amount will be delivered to customers beginning on Friday and throughout September, many iPhone pre-orders are scheduled to be delivered in October," Apple said in a statement.
Apple last week unveiled the iPhone 6 and iPhone 6 Plus, in a move aimed at satisfying consumer preference for bigger smartphone displays.
The announcement means Apple may see shortages and long lines at its retail stores when sales begin on Friday.
Sales are set to open at 8 am local time in the US, Australia, Canada, France, Germany, Hong Kong, Japan, Puerto Rico, Singapore and Britain. Some 20 more countries will get the iPhone September 26.
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Some of the new iPhones will also be available from carriers and other retailers.
Apple last Tuesday unveiled its first smartwatch and two large-screen versions of the iPhone, in a move to recapture its role as a trend-setter.
New iPhone 6 models boost screen sizes in what some see as the company catching up to a "phablet" trend combining features of smartphones and tablets.
The frenzy at Apple's website on Friday indicated that in the eyes of myriad iPhone lovers, bigger is indeed better.
Apple's main rival Samsung has long had a range of larger handsets and has tried to market a smartwatch of its own.
The iPhone 6 will have a screen of 4.7 inches and the 6-Plus will be 5.5 inches, allowing Apple to adapt to consumers' apparent preference for bigger displays.