Apple (Nasdaq: AAPL) says it sold 9 million iPhones in the weekend debut of two new models, almost double the previous record, and predicted that quarterly revenue would be at the high end of its previously projected range.

Sales reached record territory even amid supply constraints for the high-end version of the device, Apple said today in a statement. Analysts estimated the company would sell 5 million to 7.75 million units of the upgraded iPhone 5S and multicolor 5C models. Gross margin also will be at the top end of a prior forecast, the Cupertino, California-based company said.

The company says demand for iPhone 5s has exceeded the initial supply, and many online orders are scheduled to be shipped in the coming weeks.

Wall Street hadn’t been enthusiastic about the new models, which were unveiled earlier this month.

“While we’ve sold out of our initial supply of iPhone 5s, stores continue to receive new iPhone shipments regularly,” Chief Executive Officer Tim Cook said in the statement. “We appreciate everyone’s patience and are working hard to build enough new iPhones for everyone.”

Apple’s shares rose as much as 6.3 percent, the biggest intraday jump since November, as the results alleviated investor concern about a slump at the world’s largest technology company. The iPhone is Apple’s most important product, accounting for half its sales. The company has seen its revenue and profit growth slow and has ceded market share in the $280 billion smartphone market to Samsung Electronics Co. and other rivals.

Chinese Rollout

The smartphones went on sale Sept. 20 in U.S., Australia, Canada, China, France, Germany, Hong Kong, Japan, Puerto Rico, Singapore and the U.K. It’s the first time Apple rolled out its flagship product in China on the same day as elsewhere, abandoning the usual three-month delay, as the company seeks to lure new customers in the world’s largest mobile-phone market.

The more feature-rich iPhone 5s has an improved camera, fingerprint-reader and faster processor. It comes in three color variations — black/gray, white/silver and white/gold — and costs $199 to $399 in the U.S. with a two-year wireless contract. The less-expensive 5c model is a reconfigured version of last year’s iPhone with a plastic casing that comes in five colors. It starts at $99 with a contract.

In a separate filing, Apple said it expects total revenue for the current quarter to be near the high end of its forecast of $34 billion to $37 billion. Gross margin, the portion of sales remaining after deducting product costs, will be near the high end of a range of 36 percent to 37 percent.

The stock rose 5.5 percent to $493.01 at 9:52 a.m. in New York after climbing as high as $496.91. Apple shares had declined 12 percent this year before today, compared with a 20 percent gain for the Standard & Poor’s 500 Index.

Long Lines

Shoppers lined up at Apple Stores in New York, Munich, Tokyo and other cities, with some waiting for days to get their hands on the new models. The gold version emerged as the hottest seller, and AT&T Inc., Sprint Corp., T-Mobile US Inc. and Verizon Wireless won’t be able to ship gold iPhones until October, while the others are available this month, Apple said on its website.

Sales and profit growth has decelerated at Apple in the absence of major new product categories, and the company is counting on the new iPhone designs to lure new customers and spur growth.

Apple also said its fourth-quarter revenue will be at the high end of its estimates. The company had projected $34 billion to $37 billion in total revenue, and it also said gross margins will be near the high end of its expectations.

FactSet says analysts were forecasting $36.17 billion in revenue.

Shares of Apple gained $30.37, or 6.5 percent, to $497.78 in premarket trading. The Cupertino, Calif., company’s stock is down about 12 percent in 2013 and has lost almost third of its value over the last year.