Apple said a significant number of orders will be delivered to customers beginning Friday, but many will be shipped in October as demand outstrips supply.
The first-day pre-orders for the new iPhones, which feature larger screens, were double the two million orders for iPhone 5 models in 2012.
"We attribute this (pre-order numbers) to the large pent-up demand for larger screens on the iPhone...," Janney Capital Markets analysts wrote in a note.
The brokerage raised its unit sales estimate for the latest iPhones to 37.4 million for the fourth quarter and 60 million for the first quarter.
While Apple did not break out first-day pre-orders for iPhone 5Ss and 5Cs launched last year, it sold 9 million of those phones in the first three days in stores as China joined the list of launch countries for the first time.
The company said the new iPhone models will be available to customers in its stores in the United States, Canada, Australia and some other countries on Friday morning.
AT&T Inc, Sprint Corp, T-Mobile US Inc and Verizon Wireless and some Apple authorized resellers will also start selling the phones on Friday.
Apple's website showed last week that the larger 5.5-inch "Plus" models displayed a wait time of up to a month. The 4.7-inch version was available for delivery on Sept. 19.
The company routinely grapples with iPhone supply constraints, particularly in years that involve a smartphone re-design.
Apple's shares were up less than 1 percent at $101.94 in early trading on Monday.
(Reporting By Lehar Maan and Soham Chatterjee in Bangalore)
iPhone's pay system may not be a game changer
iPhone 6 Plus shipments delayed amid record orders
Will Apple's latest iPhones have takers? The jury is out
Pakistan flood death toll crosses 300
Massive dewatering operations in Srinagar, 2.26 lakh people rescued