The probe comes as top politicians are ratcheting up warnings against the US group, with the German justice ministry mulling possible penalties if Facebook failed to remove offensive user commentaries promptly after they have been flagged.
Concern has been rising over the vitriolic comments made by some Facebook and Twitter users in Germany, which have gained intensity as public misgivings grow in some quarters over the almost 900,000 asylum seekers who arrived last year.
His service is examining if it is the "competent office for such claims and whether there has been criminal conduct", he said, adding that investigators are looking into whether German penal law applies in this case.
Lawyer Chan-jo Jun, who initiated the claim, said he had compiled a list of 438 cases including incitement of hate and violence as well as support for terrorist groups made on Facebook, but which he said the social network has failed to delete even though they have been repeatedly flagged up as offensive speech.
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Jun last year filed a similar challenge in the northern city of Hamburg but prosecutors there rejected the claim, saying that Facebook managers did not fall under German jurisdiction.
Facebook declined comment on the probe but said "the allegations lack merit and there has been no violation of German law by Facebook or its employees."