Unprecedented demand for Apple’s larger-screen iPhone 6 and iPhone Plus drove more than 4 million orders for the new smartphones in the first 24 hours — a record that depleted its inventory, the tech giant said Monday.

But many customers will have to wait a month or so for their new iPhones to arrive. While a “significant amount” will be delivered to customers beginning Friday, Sept. 19, and through the end of the month, many iPhone pre-orders are scheduled to be delivered in October, Apple said.

The iPhone 6 smartphones, unveiled last week, went on sale at Apple.com and through carrier partners at 3 a.m. Eastern Friday. Despite reports of order glitches, Apple said initial sales were the best ever for its iconic phones. Apple’s previous self-reported record was more than 2 million pre-orders for the iPhone 5 in September 2012.

The iPhone 6 has a 4.7-inch screen and the iPhone 6 Plus has a 5.5-inch Retina HD displays, with glass that covers the entire surface and curves around the edges of the thinner devices. The smartphones also feature a 64-bit A8 chip, which Apple claimed makes graphics performance 84 times faster than the original iPhone launched in 2007.

The new models “are better in every way, and we are thrilled customers love them as much as we do,” Apple CEO Tim Cook said in a statement.

According to Apple, it will have additional supplies of the iPhone 6 units available to walk-in customers at Apple retail stores in the U.S. on Friday, Sept. 19, at 8 a.m. local time. Both models also will be available on Friday from AT&T, Sprint, T-Mobile, Verizon Wireless, additional carriers and resellers.

In addition to the U.S., Apple said the iPhone 6 smartphones will be available starting Sept. 19 in the U.K., Australia, Canada, France, Germany, Hong Kong, Japan, Puerto Rico and Singapore. The phones are slated to go on sale in more than 20 additional countries Sept. 26.

The iPhone 6 features iOS 8, the latest device operating system with a string of enhancements. The smartphones also mark the debut of Apple Pay, a new mobile-payments system that supports credit and debit cards from American Express, MasterCard and Visa issued by major banks, with payments supported by retailers including Bloomingdale’s, Disney Store and Walt Disney World Resort, Duane Reade, Macy’s, McDonald’s, Staples, Subway, Walgreens and Whole Foods Market.