The Vision in 3D competition runs until September 2, and tasks 3DS users with creating a 60-second film with a British summer theme.
Successful candidates must be British and make "clever use" of the system's 3D technology.
The winner will be decided by a panel made up of AV artist Stuart Warren-Hill and Senna director Asif Kapadia.
The winning entry will have the chance to shoot a new 3D short film that will be shown before Nintendo's Gala screening at the BFI London Film Festival in October.
Three runners-up will receive a pair of tickets to the BFI London Film Festival, as well as a membership to the organisation or a Sight and Sound Magazine subscription for under-18s.
Scott, one of the competition's backers, said: "Digital and 3D filmmaking is within the grasp of everyone these days.
"I'm excited by all the skill and talent that's emerging in the UK, telling stories in different ways and it's vital that it gets our support.
"This competition launched by the BFI and Nintendo opens up a big opportunity for emerging filmmakers to make their mark and they should grab it with both hands. I can't wait to see the results."
Aspiring filmmakers are encouraged to visit the competition's website for more information on how to submit videos.
Earlier this year, Nintendo launched a 3D photography competition, involving the likes of The Saturdays and Bill Oddie.
Nintendo had previously supplied the Louvre museum in Paris with 5,000 3DS gaming systems.
Gallery - view images of the 3DS photography competition below: