The initiative is monitored by a branch of the German security service in case it violates constitutional rules on religious freedom.
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According to the report, the campaign is led by a Cologne-based cleric, Ibrahim Abou Nagie, who said he wants to save non-Muslims from hell.
The Interior Ministry in the German state of North Rhine-Westphalia said the campaign was a form of aggressive proselytizing.
So far, about 300,000 German-language copies of Islam's holy book have been given away in urban areas. Additional copies are also being distributed in Austria and Switzerland.
Salafism is considered a very conservative movement in Islam whose members try to emulate the earliest followers of Prophet Muhammad.
'Aggressive action must be stopped'
The Koran giveaway has drawn much criticism from politicians across the political spectrum in Germany.
"Wherever possible, this aggressive action must be stopped," Guenter Krings of the governing center-right Christian Democratic Union (CDU), told the Rheinische Post newspaper, the BBC reported.
Krings admitted that handing out religious material was not in itself objectionable, but said the "Salafist radicals" were disturbing the religious peace with their behavior.
The center-left Social Democrats and the Green Party have also expressed their concern.
"What is presented as the simple distribution of the Koran is in truth the subtle spreading of the Salafist ideology," said a spokesman for North Rhine-Westphalia's Interior Ministry.
According to the BBC, the project has been funded by Koran sales to Muslims and through contributions made by wealthy donors based in Bahrain.
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