Finnish game company Rovio today announced that its new smartphone and tablet game — Angry Birds Space — has hit 50 million downloads in 35 days, making it what the company believes is the fastest growing mobile game available today.

The game, which is available on iOS, Android and BlackBerry devices, as well as the Mac App Store and on PC, launched on March 22 and raced to 10 million downloads in under three days, reaching 20 million in its first week.

Rovio says it is “thrilled” to see such an ethusiastic response to the game, adding that it is concentrating on creating “fun new experiences that everybody can enjoy.”

The company also teased something bigger is coming, stating in its blog post that “There’s only one conclusion to draw: something even bigger is on its way.”

What that means is not yet known, but it could mean an announcement related to its feature film or weekly cartoon series (which we covered here) or possibly a huge download milestone.

We have reached out to the company for clarification and will update should we receive a reply.