The European Union of Jewish Students and HateAid criticised what they described as a lack of moderation regarding content which could incite hatred.
The complaint, filed at a Berlin court, concerns six posts which the groups said were anti-Semitic but not deleted even though they were reported. In one case, the deleting of a post which denied the Holocaust was explicitly refused, said the groups.
Holocaust denial is a crime in Germany.
In a statement, HateAid and the EUJS said they were trying to establish whether Twitter users have a legal right to enforce Twitter’s terms and conditions, such as not tolerating threats and hateful behaviour.
Twitter did not immediately reply to a request for a comment.