Apple's website had intermittent outages last Friday because of heavy traffic as orders began online. The company said the 4 million orders set a new 24-hour record, beating the 2 million orders in 2012. That was for the iPhone 5, the previous time Apple increased the iPhone's screen size.
Last year, Apple sold 9 million iPhone 5s and iPhone 5c phones in the first three days they were on sale, but the company didn't say how many came in the first 24 hours of advance orders.
The iPhone 5, 5s and 5c have screens measuring 4 inches diagonally. The iPhone 6 is 4.7 inches, and the iPhone 6 Plus is 5.5 inches.
Besides larger screens, the new phones announced last week offer faster performance and a wireless chip for making credit card payments at retail stores by holding the phone near the payment terminal. The phones start at $199 with a two-year service contact.
The new phones will initially be available in the U.S., Australia, Canada, France, Germany, Hong Kong, Japan, Puerto Rico, Singapore and the U.K. Availability will expand to more than 20 additional countries a week later.
A free update to Apple's iOS software for mobile devices will be available to existing users on Wednesday. The new phones will come with the update, known as iOS 8.
Apple's stock rose 30 cents to $101.96 in midday trading Monday.