The German Police Trade Union (DPoIG) demanded that individuals who try to attack another person with a knife should be prosecuted under attempted murder provisions, German magazine Spiegel reported.
So far, such attacks have been classified as a dangerous bodily injury, which is a far lighter offense and subject to a less severe punishment.
The union also called on the authorities to compile nationwide statistics on knife incidents.
The demands, directed at the new federal Justice Minister Katarina Barley and Interior Minister Horst Seehofer, come amid several deadly stabbings which have taken place in Germany recently.
In January, a 30-year-old Afghan asylum seeker attacked and killed his compatriot, a 38-year-old woman, by stabbing her 16 times with a 20-centimeter knife near a supermarket in the German city of Prien because she had converted to Christianity.
Earlier, in December, a 15-year-old Afghan boy murdered a German girl in a grocery store in the German town of Kandel in the course of an argument.
A few days before that, a 19-year-old refugee tried to drown his 17-year-old German ex-girlfriend in the Havel River, in Berlin. The girl managed to survive. The two were formerly a couple and the crime was said to be the result of a breakup.