Orders for the iPhone 5 topped 2 million in their first 24 hours, more than double the amount of its predecessor over the same period.
Apple started taking iPhone 5 orders at 3am EDT on Friday.
The company also says that while most orders will be delivered on Friday, demand for the iPhone 5 exceeds the initial supply, so some of the devices are scheduled for delivery in October.
The Cupertino, California company's stock added US$7 to US$698.28 in morning trading after rising as high as US$699.54 earlier in the session.
The iPhone 5 has a bigger screen - four inches (10.16 centimetres) measured diagonally - that allows room for another row of icons and lets widescreen movies fit better. The calendar will now show five days at a time instead of just three. Previous iPhone models carried 3.5-inch (8.89-centimetre) screens. The phone is also thinner and weighs less than previous models.
Janney Capital Markets analyst Bill Choi said Apple's announcement Monday "suggests iPhone 5 is running well ahead of iPhone 4S". In a note to investors, Choi reaffirmed his earlier expectation that Apple will sell 7 million to 10 million iPhone 5s by the end of September.
The iPhone 5 sells for US$199 for the 16 gigabyte model, US$299 for the 32 GB or US$399 for the 64 GB model.
Apple says the iPhone 5 will be available at its 356 US stores starting Friday. Each customer that makes a purchase at a store will be offered free personal setup service, which will help them customise their device.
The phone will be available in more than 22 countries on Sept. 28.
Aside from Apple stores, the iPhone 5 will be available at Apple's website as well as through AT&T, Sprint, Verizon Wireless, some Best Buy, RadioShack, Target and Walmart stores and certain Apple authorised resellers.
Earlier Monday AT&T Inc. said it set a sales record for the iPhone 5, with customers ordering more of them than any previous iPhone model on the first day of orders and over the weekend.