The phone was launched Friday. In its first weekend, it was sold in 11 markets, which includes two more markets than previous Apple launches.
Apple Chief Executive Officer Tim Cook said initial supplies of the iPhone 5s have been sold out. However, "stores continue to receive new iPhone shipments regularly," he said.
"We appreciate everyone's patience and are working hard to build enough new iPhones for everyone," Cook said in a statement.
The iPhone 5s was made available in Britain, Australia, Canada, France, Germany, Japan, Puerto Rico, Singapore, the United States and China, including Hong Kong.
The iPhone 5s includes an upgraded camera, new color options and a fingerprint scanner that owners can use for added security.
Apple said the software upgrades were the "most significant since the original iPhone,"
The higher-priced iPhone 5s comes in gold, silver "or space gray." Priced according to memory, the 16GB model has a suggested retail price of $199. The 32GB model has a suggested price of $299, while the top-end 64 GB iPhone 5s is expected to sell for $399.
The less expensive 5c model comes in a variety of colors with a suggested price of $99 for the 16GB model and $199 for the 32GB model.