Apple claims it sold 1.7 million iPhone 4s in its first three days, outstripping analysts' forecasts and setting a record for a new version of the device.
On the first day, Apple reported pre-orders of 600,000, wiping out initial iPhone 4 stocks.
Analysts predicted the iPhone 4 would reach sales of one million to two million by 26 June - the end of Apple's fiscal quarter, according to US reports.
Apple's report of record sales comes amid reports that some iPhone 4 customers are having reception problems when they cover the bottom left corner of the device with their palm.
But Apple has shrugged off the complaints and recommended holding the phone differently or using a case to solve the problem.
The iPhone 4 went on sale in the US, UK, Japan, France and Germany on 24 June, but many stores sold out quickly to top the one million units sold at the launch of the 3GS model.
"This is the most successful product launch in Apple's history," Apple chief executive Steve Jobs said.
He apologised to customers who have been turned away from stores because of a lack of supplies.
The iPhone 4 will be available in 18 more countries by the end of July and a total of 88 countries by the end of September.