The kp/31 Suomi submachine gun in Finnish service was an outstanding weapon, but it was slow and expensive to manufacture. When Finnish forces began capturing Soviet PPS-42 and PPS-43 submachine guns form the Soviets in the Continuation War, it was very quickly decided that Finland should copy the design. This was a far simpler, far cheaper stamped sheet metal design that was not as refined as the Suomi, but much more efficient to make.

The Sudayev design was changed only minimally; primarily to fit the Finnish cartridge (9x19mm Parabellum) and magazines. They guns were originally designed to use the 50-round quad-stack boxes and 71/72 round drums of the Suomi, but also used the Swedish Carl Gustaf m/45 magazine that was adopted by Finland after WW2.

Two companies were approached to produce the M44; Tikkakoski and Ammus Oy. Ammus was unable to source raw materials for the project, and only Tikka put the guns into production. Marshal Mannerheim initially wanted 50,000, but the order was reduced to 20,000 - of which only 10,000 were actually made, due to limited material availability before the end of the war led to production ending. Another 400 were assembled from remaining parts after the war.

In the 1950s, a plan was begun to resume M44 production in order to completely replace the Suomi in Finnish inventory. However, this plan was interrupted when Sam Cummings of InterArms made a deal to trade Finland about 75,000 surplus Sten guns for Finland's supply of 7.35mm Carcano rifle (received as aid form Italy during the war) along with a melange of old machine guns. This was a sufficient quantity of Stens to handle the duties of the Suomi, and so the Sten went into Finnish service and M44 production was never resumed.

Those Carcano rifles were in turn imported into the United States, and this is why the majority of 7.35mm Carcano here bear Finnish "SA" property stamps. The same is true for the significant number of Chauchat automatic rifles in the US with Finnish property marks, which were also part of the deal.