Early sales are a good sign for BlackBerry, but the race is just beginning. (Mark Lennihan/AP)

BlackBerry has been upbeat about sales of its new smartphones, saying that sales in Canada and Great Britain — two strong markets for the company — have been going great.

Chief Executive Thorsten Heins said that this week’s launch in Canada was the “best day ever” for a new BlackBerry smartphone, though the company didn’t provide any specific numbers. Heins also said that sales in Britain have nearly tripled the company’s best debut week smartphone sales — again, without specifics.

BlackBerry, formerly Research in Motion, has made no secret that it’s got its eye on the bronze medal of the smartphone market, behind Apple’s iOS and Google’s Android. Taking on either of the big two would be an impossible, demoralizing goal for the once-dominant Canadian smartphone maker, but holding on as a solid third choice is an achievable goal.

But not an easy one. BlackBerry’s greatest rival right now isn’t Apple of Google — it’s Microsoft.

Both companies are going after the business market in a big way. Microsoft is touting integration with its PCs and other services, saying that consumers can benefit from its whole ecosystem. BlackBerry meanwhile, is pitching its reputation for security and snazzy new phones with more moden designs.

Microsoft launched a new smartphone operating system in October, Windows Phone 8. Sales seem to be going better than expected, particularly for flagship devices such as the Nokia Lumia line. That sets up quite the obstacle for BlackBerry.

According to the analysis firm Strategic Analytics, Microsoft overtook BlackBerry in the fourth quarter of 2012 as the number-three platform for the first time since 2006. Data from Kantar backs that ranking up, Boy Genius Report noted, though data from comScore indicates that BlackBerry still has the third-place spot.

In any case, the race is a close one. And international success is certainly no indication that BlackBerry will find a hit in the U.S. — one of its most critical markets. Even with early indications that BlackBerry is finding some pent-up demand worldwide, it’s still very early in the race.

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Ten things to know about BlackBerry

BlackBerry 10: Research in Motion gets new name, launches new system, new phones

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