Davutoglu's comments came in an interview with the Frankfurter Allgemeine Zeitung published on Wednesday, as recently formed PEGIDA (Patriotic Europeans Against the Islamization of the West) continues to make headlines with the significant increases in support it has achieved within just months.
Davutoglu told the German daily: "When terrorist groups destroyed churches in Mossul, they believed that it was an Islamic city only for Muslims, but that was not true."
"Throughout history, Christian also lived there. This is the same logic of PEGIDA which argues that Germany only belongs to Christians."
"That is a medieval mentality," he said, criticizing PEGIDA’s rejection of cultural diversity and its anti-Islam and anti-immigration rhetoric.
The group started weekly protests in Dresden in October with around 500 protesters, but on Monday more than 25,000 protesters attended PEGIDA’s rally in Dresden.
- 'Threat for Turks'
PEGIDA has attracted far-right and right-wing groups as well as citizens unaffiliated to a political party or group.
Davutoglu went on: "We have serious concerns over PEGIDA. These people wish for an exclusively Christian German society."
"That is not only a threat for Turks and Muslims, but also a threat for Germany itself."
The Turkish Prime Minister underlined that, soon after the economic crisis in Germany in 1929, people looked for culprits, for someone to blame, among those they perceived as "the other".
The popular discontent was exploited by Adolf Hitler's Nazi Party in the 1930s and led to extermination policies against the Jews.
About six million Jews died through genocide carried out in death camps across Nazi Germany.
- 'Looking for culprits'
Davutoglu warned against the current dangerous trend of looking for culprits for economic or social problems, and said that this were further similarities between PEGIDA and ISIL.
“Looking for culprits among the others …That is exactly the mentality of Daesh (ISIL). A pre-modern name for that can be Daesh, a modern name for that is PEGIDA,” he said.
He thanked German Chancellor Angela Merkel for her remarks on Monday, when she stressed that Islam was also a part of Germany.
Davutoglu underlined that Turkish immigrants living in Germany had successfully integrated into society despite many obstacles.
“If we would like to make further progress in integration, we should focus on the success stories. But people often see first the negative aspects,” Davutoglu said.
Germany has the second-largest Muslim population in Western Europe, after France.
- Perceived threat
Among the four million Muslims in the country, three million are of Turkish origin.
Germany witnessed an increase in suspicion and negative feelings towards Muslims in recent months as fa-right and right-wing populist parties sought to benefit from a growing fear of Islam and Muslims.
A recent study by the Bertelsmann Foundation has revealed that Germans have become more intolerant towards Islam in recent years and developed a prejudiced opinion of Muslim immigrants.
A total of 57 percent of Germany’s non-Muslims said in a representative poll in Nov. 2014 that they perceived Islam as a threat - a rise of four percent since 2012.
Sixty one percent of Germans said they believed Islam was not compatible with life in the Western world, representing a nine percent increase from 2012.
Forty percent said that they did not feel at home in their own country because of what they perceived to be the "Islamization" of the nation.