The figures from Apple appeared to defy predictions from its critics that the company is losing momentum in the smartphone market and in innovation.
"Apple gets the last laugh," said Roger Kay, analyst at Endpoint Technologies Associates, in a tweet.
Apple said demand has exceeded the supply for the new handsets, and that some customers will have to wait.
"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," Cook said.
"We appreciate everyone's patience and are working hard to build enough new iPhones for everyone."
Apple began worldwide sales Friday of the high-end iPhone 5S and a lower-cost iPhone 5C, drawing crowds from Australia to Tokyo to Paris to New York.
The new phones are being sold in the United States, Britain, Australia, Canada, China, France, Germany, Hong Kong, Japan, Puerto Rico and Singapore.
Apple also said more than 200 million of its smartphones and tablets are now running the redesigned operating system iOS 7, "making it the fastest software upgrade in history."
The new operating system has a bolder look, and includes the free iTunes Radio launched by Apple. It is a free upgrade for a number of iPhones and iPads sold in the past couple of years.
Apple said in a filing with the Securities and Exchange Commission that with the strong response to the new iPhones, it now expects revenue for the fourth fiscal quarter to be "near the high end of the previously provided range of $34 billion to $37 billion," and that profit margins will also be near the high end of its estimate of 36 to 37%.
Apple shares, which have been under pressure in recent months, shot up 4.4% in early trades to $488.11.
The news from Apple "implies a message from management that the company is back on track," said Ben Reitzes at Barclays.
Telecom analyst Jeff Kagan called the sales "stellar" but said Apple may have boosted the numbers by not allowing pre-orders for the iPhone 5S.
"Apple was concerned about the public relations angle of a soft first weekend, so they took some steps to strengthen the numbers," Kagan said in an email.
"Traditionally users could pre-order devices. Not this year. This year anyone who wanted a new iPhone, must get into line. That bolstered the lines and strengthened opening weekend from a PR perspective. This upset users, but made for great numbers."
Apple faced criticism for not cutting the price of its iPhone 5C as much as some had expected to appeal to emerging markets and budget-conscious buyers. The lower-cost iPhone sold for $99 in the United States with a carrier subsidy, but $549 without that, and more in other countries.
Brian White at Cantor Fitzgerald said Apple's sales data "highlights the strong demand around the new iPhone 5C that, in our opinion, undeservedly received unfair criticism at launch."
A survey by the research firm Localytics said the more expensive iPhone 5S was outselling the 5C in the US market by a margin of more than three to one, and by a five-to-one margin in Japan.
"This makes sense, since those who feel the need to buy a new device the very weekend it launches are most likely the power users who want the highest-end phone experience," said Localytics analyst Bernd Leger.
"It's not altogether clear whether poorer countries are buying more 5c's compared to 5s's, but it will be good to keep a close eye on this data in the next few days to see if there is any pattern emerging."