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Vincent Yu, AP
In this photo taken on Friday, Sept. 19, 2014, people wait to buy the new Apple iPhone 6 and 6 Plus devices outside an Apple store in Hong Kong.

SAN FRANCISCO — Apple sold a record of more than 10 million iPhones in the weekend debut of two new models, as consumers flocked to stores and Web shops to buy handsets featuring bigger screens.

Sales surpassed last year's 9 million units when the iPhone 5s and 5c were introduced, the Cupertino, California-based company said in a statement Monday.

"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," Chief Executive Officer Tim Cook said in the statement.

Analysts' estimates varied widely, with one projecting sales as high as 15 million units while others had cautioned that the results could fall short of last year's shipments of the new iPhone 5s and 5c because of production shortages and the fact that the new devices didn't go on sale in China.

Cook is using the iPhone 6, which has a 4.7-inch (11.9 centimeters) display, and iPhone 6 Plus with a 5.5-inch screen to push into the turf of Samsung Electronics, HTC and other manufacturers of jumbo-sized smartphones. The rollout of the new iPhones, which account for more than half of Apple's $171 billion in annual revenue, will be followed by the anticipated debut of new iPad models next month as the company revamps its product lineup ahead of the holiday shopping season.

The new iPhones arrived in Apple stores on Sept. 19 in the United States, Australia, Canada, France, Germany, Hong Kong, Japan, Puerto Rico, Singapore and Britain.

Demand is robust. Pre-orders of the latest models topped 4 million units in the first 24 hours. A third of Android users polled by Boston-based Gazelle Inc. said they're likely to upgrade to the iPhone 6, up from a 10th a year ago when the iPhone 5s and 5c went on sale, according to Chris Sullivan, Gazelle's CEO.

IPhone sales exceeded expectations for the first weekend, "shattering all previous sell-through records by a large margin," Cook said.

From the beginning there were concerns that Apple would run out of inventory. Manufacturing the 5.5-inch model is more complicated than the smaller version, resulting in lower output, a person familiar with the process has said. Some stores in the U.S. on the first day didn't have any of the largest iPhones left.

Carl Howe, an analyst at 451 Research, had estimated that Apple would sell 12 million to 15 million new devices during the first weekend, while Toni Sacconaghi, an analyst at Sanford C. Bernstein & Co., projected sales of 7 million to 8 million because of supply constraints and China not being one of the first countries selling the devices.

The next wave of sales start Sept. 26 in Austria, Belgium, Denmark, Finland, Ireland, Isle of Man, Italy, Liechtenstein, Luxembourg, Netherlands, New Zealand, Norway, Portugal, Qatar, Russia, Saudi Arabia, Spain, Sweden, Switzerland, Taiwan, Turkey and United Arab Emirates, according to Apple. Eventually, the new handsets will be available in 115 countries by year's end, according to the company.