NEW YORK — BlackBerrys still fly off the shelves. They still convey the message that their owners mean business – that they’re people who are important enough to need e-mail access all the time.

But BlackBerrys are now being challenged by phones that say you can have your e-mail and have fun, too.

Research In Motion Ltd., the maker of the BlackBerry, revealed a new phone Tuesday that says the company is still in the game, but it’s doing so by catching up to the competition rather than by breaking new ground.

The Torch will be RIM’s first device with both a touch screen and the BlackBerry’s signature full-alphabet keypad. It hits AT&T stores on Aug. 12 for $199 with a two-year contract.

Meanwhile, RIM is scrambling to deal with suspicion from foreign governments threatened by the very thing that’s made the phones such a success in the corporate market: The assurance that a user’s e-mail is private.

The United Arab Emirates announced over the weekend that it would block BlackBerry e-mail, messaging and Web browsing services starting in October because authorities don’t have enough access to communications from the devices. On Tuesday, Saudi Arabia’s state news agency SPA said that the country’s telecom regulator has informed mobile service providers that they must halt BlackBerry services in the country starting Friday.

The conflicts pit national security against corporate security, and BlackBerry is caught in the middle. The company is closemouthed about the issue, hoping that quiet negotiations will resolve it, as they have in the past. At the same time, it is reassuring corporate customers that their e-mails are safe from snooping foreign governments.

RIM, which is based in Waterloo, Ontario, sold its 100 millionth BlackBerry this year. It’s still the most popular smart phone in the United States, ahead of the iPhone. It’s been holding its own against Apple Inc.’s phone, but in the past year, a new challenger has zoomed out of nowhere to put a dent in its market share: Google Inc.’s Android software, used by several phone manufacturers, including HTC Corp. and Motorola Inc.

RIM has had success expanding the appeal of the BlackBerry beyond the corporate world to consumers. The question is now whether it can hold on to its core constituents in corporate information-technology departments.

IT people like BlackBerrys because they’re relatively secure and easy to manage. But that also means they’re locked down in ways that frustrate their users, who may not be able to install the third-party applications they want.

RIM shares have fallen more than 25 percent since April because of fears that the iPhone would take over in the corporate world. Shares fell $1.45, or 2.5 percent, to close Tuesday at $55.53.