Shoppers said they were met with error messages on the company Web sites, and lines formed in stores as clerks tried to get orders into their systems.
Computer systems at Apple Inc., the maker of the phone, or AT&T Inc., its exclusive U.S. carrier, have had various problems meeting demand for the iPhone every year since the first one launched, in 2007.
Neither Apple nor AT&T commented on the latest problems. They come a week after AT&T plugged an embarrasing security hole on its Web site, which exposed the e-mail addresses of people who had bought another Apple product, the iPad 3G.
Japanese phone company Softbank started taking orders earlier in the day, and was also flooded with requests. Softbank spokesman Furuya Katsuhide said that the better-than-expected demand had stressed the company's systems, which slowed both its Web site and the reservation process at stores.
The iPhone 4 goes on sale June 24 starting at $199. It will feature a higher-resolution screen, longer battery life and thinner design than last year's model.