Research In Motion Ltd., which is preparing to unveil its BlackBerry 10 phones later this month, says more than 1,600 North American businesses have registered for a training program for the new handsets and software.

Of the registered customers, more than 1,000 have already begun using the BlackBerry 10 Ready program since its introduction in early December, said Bryan Lee, RIM’s (Nasdaq: RIMM) senior director of enterprise accounts.

The news is another boost for RIM, which was helped last week at the Consumer Electronics Show when the largest wireless providers in the U.S. said they would offer the new BlackBerry devices. 

The customers include Fortune 500 companies, law firms, schools, universities, retailers and government agencies, he said.

“We’re very encouraged by the participation of the types of customers,” Lee said in a phone interview. The companies are expected to be the first adopters once the phones are commercially available, he said.

RIM will debut the first of the BlackBerry 10 models at an event on Jan. 30, before putting them on sale in February and March.

The stock has more than doubled since late September on rising optimism that BlackBerry 10 will help RIM win back market share from rivals such as Apple Inc.

Shares of the Waterloo, Ontario-based company rose 3.8 percent to $15.03 at 11:15 a.m. in New York. The stock jumped as much as 6.1 percent earlier in the session.

One of the goals of the training is to integrate the BlackBerry Enterprise Server software that RIM offers to corporate clients with their own information-technology systems, Lee said.

RIM said in its 2012 annual report that it had more than 250,000 BlackBerry Enterprise servers deployed around the world. Lee didn’t have figures on the scale of BlackBerry 10 training outside North America.

RIM is targeting its “whole base” to sign up for BB10 training, he said. “Obviously we want get to our existing customers and make sure we shout this from the rooftops.”

RIM also operates a research and development office in the Research Triangle Park, N.C. area.