SAN FRANCISCO — Apple rolled out a high-definition iPad on Wednesday with a faster processor, a better camera and a display screen that promises to be dramatically sharper than the current model, the iPad 2.

“It is amazing,” Apple CEO Tim Cook said at a San Francisco unveiling. “We’ve taken it to a whole new level, and we are redefining the category that Apple created with the original iPad.”

The new 9.7-inch display screen will feature a “retina display” of 2047 by 1536 pixels, compared with the current model’s 1024 by 768 pixels.

To break it down, that’s a total of 3.1 million pixels on the display screen.

“Your retina in your eye cannot discern those individual pixels,” said Apple Senior Vice President Phil Schiller. “The images on it look stunning.”

The new iPad will be available in the United States and 9 other countries March 16 and cost the same as the iPad 2 — from $499 to $829 based on storage capacity and internet connections. Pre-orders were opened at Apple’s online store on Wednesday.

The new version will be available in the U.S. on AT&T and Verizon and will be the first iPad to connect to 4G networks (a fact that, at least for now, remains academic in most cities). It also will go on sale Friday in Australia, Canada, France, Germany, Hong Kong, Japan, Puerto Rico, Singapore, Switzerland, the UK and the U.S. Virgin Islands.

“This new iPad has the most wireless bands of any device that has ever shipped, and it is truly revolutionary,” Schiller said.

And the new iPad will be the first to run on 4G wireless networks, a source familiar with the device’s specifications told CNNMoney on Wednesday.

It will have a a 5-megapixel camera, representing a significant leap from the current iPad’s so-so lens.

Surprisingly, “the new iPad” was as close to a name as Apple gave the gadget Wednesday. Predictions had bounced back and forth between “iPad 3” and “iPad HD” before the event. But the announcement ended without an official name being announced.

Whether that means Apple plans to abandon an iPhone-like naming routine (iPhone, iPhone 3G, iPhone 3GS, iPhone 4, iPhone 4S) in favor of occasional upgrades to “the iPad” remains to be seen.

On Wednesday, Cook also announced an updated version of Apple TV, the company’s Web-TV integration device that competes with products like Google TV, Roku and Boxee.

The system supports 1080p, or “Full HD” high-definition video, up from the current model’s 720p. It will be available for $99 starting next week and could pave the way for what’s expected to be Apple’s next project: a fully integrated high-definition television.

“Across the year, you’re going to see a lot more of this kind of innovation,” Cook teased at the end of Wednesday’s event. “We are just getting started.”

When the iPad was introduced in early 2010, tablets already existed, but none had become popular with mainstream consumers. Some analysts wondered if there would be a market for a device that falls somewhere between a smartphone and a laptop but doesn’t fully replace either.

The answer was a resounding “yes.” The company has sold more than 55 million iPads worldwide to date.

Before his death in October, Apple co-founder Steve Jobs predicted that 2011 would be the “year of the copycat” in the tablet space. In large part, it was, and that was bad news for Apple’s rivals, as competitors from HP to Samsung to Motorola tried unsuccessfully to offer a viable alternative to the iPad.

The new iPad will arrive in a somewhat trickier landscape.

By going smaller and simpler, Amazon made a splash with its Kindle Fire over the holidays, while rival bookseller Barnes & Noble countered with its popular Nook Tablet. Both devices start at $199. The new Acer Iconia A500 offers more memory than the iPad 2, while other companies have begun flooding the market with devices that are smaller and cheaper than Apple’s standard-bearer.

Just last week, Microsoft rolled out its Windows 8 operating system for tablets, suggesting that Windows-based tablets could be making a serious run.

In a move perhaps designed as a shot at these rival upstarts, Cook announced Wednesday that the price on the iPad 2 will be slashed $100. So, a 16GB, Wi-Fi-only model will sell for $399, making it more competitive with the lower-end tablets.

Apple surprised many observers last year when the iPad 2 was priced the same as the original iPad: ranging from $499 to $829, depending on 3G capability and storage capacity.

Cook also announced Wednesday that the 25 billionth app has been downloaded from the App Store. Perhaps significantly, that app was downloaded in China.