"The charge d'affaires has been summoned to the Turkish foreign ministry at 1:00 pm (local time)," a spokeswoman for the German embassy told AFP, adding that the ambassador was not in town.
Tens of thousands of supporters of President Recep Tayyip Erdogan rallied in Cologne yesterday to show their opposition to a failed coup on July 15, which aimed to unseat the Turkish leader.
Hours before the demonstration, Germany's constitutional court rejected an application to show live speeches from Turkey by politicians including Erdogan, over fears they could work up the crowd.
Germany is home to three million ethnic Turks, making up Turkey's largest diaspora, and tensions over the coup have put authorities there on edge.
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The tension comes at a time when relations between Germany and Turkey are already strained over the German parliament's decision to brand as genocide the World War I-era Armenian massacre by Ottoman forces.
Turkey's military and political leaders were meanwhile due to meet in Ankara with the top US military commander in the first direct talks since the failed coup.
Tensions between the two NATO allies have been aggravated by the foiled putsch, with some Turkish officials even alleging that Washington could have had a hand in the plot. The suggestion has been firmly denied by top US officials.
Turkey successfully thwarted the attempted coup, blaming it on a military faction loyal to Erdogan's arch-foe Fethullah Gulen, a US-based cleric who has been in self-imposed exile in the United States since 1999.
Turkey is now requesting his extradition from Pennsylvania.
"If they keep on dragging (their) feet on the Gulen issue... Then things will take a different course because events of July 15 are crystal clear."
Last week, Erdogan lashed out at the top US general in the Middle East, General Joseph Votel, after he expressed concerns about the future of military relations between the two allies in the wake of the putsch.