When the Tikkakoski company bought the rights to produce the kp31 "Suomi" submachine gun in the 1930s, they attempted to make a bunch of export sales, although none were very successful. By the late 30s more countries were interested, but by that time Finnish military needs took precedence. While a few export sales were made during World War Two, the more significant exports were in the forms of licensed production. In particular, Sweden, Switzerland, and Denmark all bought the rights to manufacture Suomis.

In Denmark, this was the Model 1941, produced by both Madsen and Hovea with approval of the German occupying authorities. About 1400 were made between the 1941 and 1943 before the Germans lost confidence in Denmark and disarmed its military. The M1941 is mechanically identical to the standard Finnish kp31 except for:

- Front sight protective wings
- Triangular front sling swivel
- Rear sling swivel (instead of a sling bar)
- Aggressive pistol-grip stock design

Interestingly several of these changes were also incorporated into Tikka's 1942 prototype improved kp31, which never saw production.