Apple sold a higher than expected 9 million iPhone 5s and iPhone 5c models in the first three days following their Friday launch.
The sales figures prompted the company to issue a more optimistic financial forecast.
Sales of the new models were nearly double those of the iPhone 5 in the first weekend after its launch a year ago. The iPhone 5 sold 5 million in its first three days on the market.
Wall Street analysts had expected Apple to sell about 6 million of the two new iPhones.
Apple tweaked its financial forecast to reflect the higher sales, an unusual move for the company. It said revenue in the fiscal fourth quarter would be near the high end of its previous forecast of $34 billion to $37 billion.
It said gross profit margin would come in at the top of its previous forecast of 36-37%.
Analysts' average revenue forecast is $36.10 billion, according to Thomson Reuters. They said that today's figures show that Apple still has a deep connection with its customers.
Demand for the iPhone 5s has exceeded initial supplies, and many online orders are scheduled to be shipped in the coming weeks, Apple said.
On Friday, long lines formed outside stores in Tokyo, New York, San Francisco and other cities around the world for the new top-of-the-line 5s and the less-expensive 5c. It was the first time Apple launched two iPhone models simultaneously.
The gold-coloured version of the 5S, which also comes in silver and grey, was sold out as of Friday and will now ship only in October, according to Apple's website. As of today, the two other colours were also set to be shipped only in October.
"The demand for the new iPhones has been incredible, and while we've sold out of our initial supply of iPhone 5s, stores continue to receive new iPhone shipments regularly," Apple's chief executive Tim Cook said in a statement.
"We appreciate everyone's patience and are working hard to build enough new iPhones for everyone,'' he added.
The company said more than 200 million iOS devices are now running the upgraded mobile operating system iOS 7, which was rolled out just before the iPhone launch.
Apple did not break out separate sales figures for the 5s and 5c. The 5s offers a touch ID that scans a user's fingerprint to unlock the phone. The 5c comes in an array of colours.
Apple for the first time simultaneously launched the new iPhones in China, a crucial market, along with the rollout in Hong Kong, Singapore, the US, Australia, Japan, UK, Canada, Germany, France and Puerto Rico.
It previously launched it phones in China a few months after the US launch.