(Reuters) - Apple Inc booked orders for over two million iPhone 5 models in the first 24 hours, reflecting a higher-than-expected demand for the consumer device giant's new smartphone and setting it up for a strong holiday quarter.

Apple shares rose in extended after-market trading to touch $700 per share for the first time. They have gained nearly 22 percent in the past 3-1/2 months in the build-up to the launch of the iPhone 5.

Apple said on Monday that pre-orders outstripped initial supply but it would deliver most phones as planned by Friday, the first day of delivery. Many would not be available until October, however.

It is not unusual for Apple products to sell out the first day but this time around Apple has doubled its first-day sales record. Last October, the company booked 1 million orders for the iPhone 4S, in the first 24 hours. That had beaten Apple's previous one-day record of 600,000 sales for the iPhone 4.

The strong preorders could mean a huge holiday quarter for Apple as the iPhone -- its marquee device -- accounts for half of Apple's revenue.

Apple will make initial deliveries of the iPhone 5 by September 21 in the United States and most of the major European markets, such as France, Germany and the United Kingdom. The phone then goes on sale on September 28 in 22 other countries.

Given the demand for the device so far and Apple's aggressive rollout of it internationally, some analysts raised their sales and earnings estimates.

"The pace of this iPhone 5 roll-out is the fastest in the iPhone's history and points to a big December quarter," said Barclays analyst Ben Reitzes, who expects Apple to sell 45.21 million iPhones in the December quarter, up 22 percent from last year. Reitzes said his estimates "could still be conservative."

Canaccord Genuity analyst Michael Walkley said he now expected Apple to ship 9 million to 10 million iPhone 5s from Friday to September 29, the last day of its fiscal 2012 year.

He also raised his earnings per share estimates for the September and December quarters to $44.32 from $43.25, and to $56.96 from $56.90, respectively.

Wall Street analysts on average expect Apple to earn $44.25 per share in the December quarter, according to Thomson Reuters I/B/E/S estimates.

The new phone, which will appear in stores on Friday for walk-in purchases, has a larger, 4-inch screen and is slimmer and far lighter than the previous model. The iPhone 5 supports the faster 4G network and also comes with a number of software updates, including Apple's new in-house maps feature.

Apple began taking orders for the iPhone 5 at midnight Pacific time on Friday (0700 GMT Saturday). Shipping dates for the smartphone slipped by a week within an hour of the start of preorders.

On Monday morning, Apple's U.S. store, at www.apple.com, showed preorders placed at that time would take two to three weeks to ship.

AT&T SETS SALES RECORD

Wall Street is also keeping a close eye on the supply of the smartphone.

"We still believe Apple is facing significant production constraints due to a move toward in-cell display technology, which pushes a significant amount of units into the December and March quarters," Reitzes said.

One of Apple's key suppliers for screens, Sharp Corp, is struggling with high costs and scrambling to raise funds to pay debt.

The latest iPhone comes as competition in the smartphone market has reached a fever-pitch with Apple up against phones that run on Google Inc's Android software. Android has become the most-used mobile operating system in the world, while Apple's key supplier and rival, Samsung Electronics, has taken the lead in smartphone sales.

But Apple appears to be making headway into the corporate market, a traditional stronghold of now-struggling Canadian company Research In Motion

Yahoo Inc has instituted a new corporate policy that allows employees to pick from a host of smartphones, including the iPhone 5 and Android-based phones such as Samsung's Galaxy S3. Yahoo, which previously gave out RIM's Blackberry phones, will no longer support them, according to Business Insider blog, which cited an internal memo from Yahoo Chief Executive Marissa Mayer.

Yahoo declined to comment.

AT&T, the No. 2 U.S. mobile service provider, said demand over the weekend had made the iPhone 5 the fastest-selling iPhone the company has ever offered.

AT&T did not disclose how many iPhones it had sold, but said the iPhone 5 was still available for preorder and would go on sale September 21 at AT&T retail stores.

All the phones carriers, including Verizon Communications Inc and Sprint Nextel Corp, showed delays of up to three weeks in shipping the phone.

European carriers also reported brisk sales. France Telecom's Orange said bookings for the new phone "have been very strong, breaking the records of what we saw for the iPhone 4 or 4S." But the carrier said it could deliver preorders on time.

Analysts have forecast that Apple will have sold more than 30 million iPhones, including older models, by the end of September.