The Die Welt daily newspaper reported Ibrahim Abou Nagie, who initiated the campaign, said he has given away 300,000 German-language Korans in the country thus far, The Local reported.
The Korans are to be distributed in 35 town centers and through the mail.
"Wherever possible, this aggressive action must be stopped," Gunter Krings, a top member of Angela Merkel's Christian Democratic Union parliamentary party, said Wednesday.
Krings told Die Welt "there is in principle nothing against the distribution of religious texts," but said the radical Salafists were, in the words of The Local, "disturbing the religious peace with their aggressive methods."
German intelligence services consider Abou Nagie a dangerous Salafist preacher, The Local said.
He hopes to give away the German-language copies of the Koran to non-Muslims as part of the campaign "Read! In the name of your Lord who created you."
The campaign is being funded by the purchase of Korans by Muslims -- with each Koran bought funding the production of one to be given away -- and by donations from wealthy people in Bahrain.
Die Welt said the version of the Koran being distributed is moderate.
But the Berlin state Office of the Protection of the Constitution said, "Salafistism is strongly radicalizing and is promoted by its followers as supposedly the only true Islam."