With inventories dwindling, Apple watchers predict a new version with faster Internet access is coming.

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Apple’s iPhone is sold out at its online stores in the U.S. and U.K., a sign that a new model with faster Internet access may be introduced soon.

“We’re currently out of stock,” Apple spokeswoman Natalie Kerris said Monday. Both the 8-gigabyte and 16- gigabyte models are unavailable.

She declined to say when Apple will replenish inventory or comment on supply at retail stores.

The shortage suggests Chief Executive Officer Steve Jobs is readying a new model, which may be unveiled during his speech at Apple’s developer conference June 9, Piper Jaffray analyst Gene Munster said in a report.

Apple’s wireless partner in the U.K. sold out Thursday after cutting prices, and the Web-surfing handset is in short supply at Apple’s retail outlets in the U.S., he said.

“The channels are running dry,” said Munster, who recommends buying Apple shares. “The limited availability is one of several indications that the release of a new model is imminent.”

AT&T, which distributes the iPhone exclusively in the U.S., has it in stock at its retail stores, spokesman Mark Siegel said.

Jobs, who has forecast sales of 10 million iPhones for this year, is expected to unveil a model that supports faster downloads from the Internet over so-called third-generation networks, Munster said.

The device, which includes an iPod music and video player, may have a switch that lets users turn on 3G access when they want faster data speeds, and shut it off when they want to conserve battery power, he said.

Apple introduced the iPhone in the U.S. last June.

Apple said Monday that Singapore Telecommunications, Southeast Asia’s largest telephone company, will offer the iPhone in four Asian markets later this year.

Singapore Telecom’s Bharti Airtel and Globe Telecom units will offer the iPhone in India and the Philippines, respectively. SingTel, as the company is known, will sell the handset in Singapore and its Sydney-based unit will offer it in Australia. Financial terms weren’t disclosed.

“We can’t wait to get this revolutionary phone in the hands of even more people around the world,” Apple’s Kerris said.

Vodafone Group agreed this month to offer the iPhone in 10 markets, including Australia, India and Italy.

America Movil, the wireless carrier controlled by Mexican billionaire Carlos Slim, said last week that it will sell the iPhone in 16 countries in Latin America and the Caribbean.

While some users may have bought iPhones in the U.S. and unlocked them for use on unauthorized wireless networks overseas, the lack of inventory suggests Apple underestimated demand, said Shaw Wu, an analyst at American Technology Research in San Francisco.

“The stock-out now is more a function of good old demand here in the U.S.,” Wu said. He expects Jobs to announce a 3G iPhone next month and to deliver large quantities in July.