The new iPhone 6 goes on sale on Sept. 19 in the United States but the company began taking online orders on Thursday.
While the larger 5.5-inch "Plus" models now display a wait time of up to a month, the 4.7-inch version remains available for delivery on Sept. 19, Apple's website showed.
Verizon Wireless, AT&T and Sprint Corp, also showed shipment delays of up to six weeks on their respective websites. Apple said the pace of orders has so far outstripped any of its previous iPhones.
Apple routinely grapples with iPhone supply constraints, particularly in years that involve a smartphone re-design. The latest iPhones come with larger screens and some analysts had anticipated that production issues may keep a lid on initial runs.
Its suppliers had scrambled to get enough screens ready because the need to redesign a key component had disrupted panel production, supply chain sources told Reuters last month.
It was unclear whether the hiccup could limit the number of phones available to consumers, the sources said at the time. Apple declined to comment on supply chain issues.
The company unveiled its latest iPhones along with a watch and a mobile payments service on Tuesday.
AT&T's chief executive of mobile and business, Ralph de la Vega, told investors at a conference in New York that iPhone 6 orders have so far surpassed orders last year and the year before.
"It is such a great thing to wake up in the morning to know that you have hundreds of thousands of orders already before you even have a cup of coffee," said the executive.
Apple's iPhones tend to incite the kind of initial buying frenzy unknown to many other brands, partly because of the company's well-honed marketing tactics.
One post on the New York City edition of Craigslist sought $10,000 the privilege to "be one of the first & few people to own this model and before the rest of the world."
New iPhones tend to get listed at stratospheric prices on various online retail sites from the United States to China, on the assumption that there's big demand from people who must get their hands on the phone from day one. That in turns fuels a grey market of dealers who buy in bulk for resale.
(Additional reporting by Marina Lopes in New York Reporting by Soham Chatterjee and Ankush Sharma in Bangalore)
Photographs, courtesy: Apple
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