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Chief Executive Tim Cook said the company could have sold even more iPhone 6 and iPhone 6 Plus models if supplies had been available.
Analysts had estimated first-weekend sales of up to 10 million iPhones, after Apple booked record pre-orders of 4 million on September 12, the day pre-orders opened.
Apple's shares were little changed at $101.03 in early trading on the Nasdaq on Monday.
The company's first-quarter revenue is likely to be 9 per cent higher than Wall Street estimates, based on reported sales and projected demand for the new iPhones, Piper Jaffray & Co analyst Gene Munster wrote in a note. He said he expected earnings per share to be 12 per cent higher than estimates.
"Despite the supply chain constraints around the iPhone 6 Plus and tightness around certain models of the iPhone 6, we believe (Monday's) strong print demonstrates that Apple executed extremely well in the face of severe supply constraints," Cantor Fitzgerald analyst Brian White wrote in a note.
First-day pre-orders of the new phones, which went on sale in 10 countries, far surpassed the 2 million first-day pre-orders for the iPhone 5 model two years ago.
"While our team managed the manufacturing ramp better than ever before, we could have sold many more iPhones with greater supply and we are working hard to fill orders as quickly as possible," Cook said in a statement.
Last year, Apple sold 9 million iPhone 5S and 5C models in 11 countries, including China, in the first weekend they were available.
Sales of the latest models in China, the world's largest smartphone market, have been delayed by regulatory issues.
Apple sold 5 million iPhone 5 handsets, 4 million iPhone 4S models and 1.7 million iPhone 4 units during the first weekend.
The company said last week that many US customers would have to wait until next month for their new iPhones due to strong demand.
Apple routinely faces iPhone supply constraints, particularly in years that involve a re-design.
The new iPhones will be available in 20 more countries on September 26, Apple said.
The shipment levels are positive, given that iPhone 6 and iPhone 6 Plus are not initially available in China, unlike iPhone 5S and 5C models, Stifel Nicolaus & Co analyst Aaron Rakers wrote in a note.
Rakers noted that the latest models would be available in 115 countries by the end of this year compared with 100 for iPhone 5S and 5C.
