Apple's iPhone 6 Plus, which has a 5.5-inch display, goes on sale in U.S. stores on Sept. 19.
Websites of Apple's carrier partners, Verizon Wireless <VZ.N>, AT&T <T.N> and Sprint Corp <S.N>, also showed delays of up to six weeks.
It was unclear whether the hiccup could limit the number of phones initially available to consumers, the sources said at the time.
Apple's Chinese customers may also have to wait until the year-end before they can buy the iPhone 6. Apple is yet to set a release date for China, the world's biggest smartphone market.
Apple unveiled its latest iPhones along with a watch and a mobile payments service on Tuesday.