Schaefer said Foreign Minister Sigmar Gabriel would interrupt his summer holidays and return to Berlin over the "dramatic escalation in Turkish actions" to determine which "further measures" could be taken.
But as Erdogan has cracked down on dissent, jailed over 100,000 and consolidated power in the year since a failed coup attempt, Germany has been a prime target of his wrath.
Turkish President Recep Tayyip Erdogan's spokesman has branded as "unfortunate" comments by the German foreign minister, including those telling Germans to exercise caution in Turkey.
It is extremely hard for German companies to make investments in Turkey under the current political climate in the country, German Economy Minister Brigitte Zypries said on Thursday.
Relations between Germany and Turkey are increasingly strained.
He said: "Unfortunately we have constant cause to talk to Turkey about civil and press freedoms". It said Turkey was Germany's No. 15 export destination and No. 16 source of imports a year ago. The Association of German Chambers of Commerce (DIHK) has already commented on Gabriel's speech, saying current developments in Turkey are likely to affect doing business in the country.
Speaking about two months before a federal election, the Social Democrat minister said the new stance had been agreed with conservative Chancellor Angela Merkel.
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The spokesman said the point had been clearly made to the ambassador that Germany considered the activists' arrests to have been both unacceptable and incomprehensible, and that Berlin wanted Steudtner released immediately.
This month, Turkey arrested rights activists including Amnesty International's Turkey head Idil Eser and German citizen Peter Steudtner on terrorism charges, which Berlin has labelled "absurd".
"We will not accept these statements and expect that soon Germany will abandon them". At 22 billion euros ($25 billion) in deliveries of mostly auto parts and chemical products, Turkey ranked in 15th place a year ago, BGA said.
The Turkey correspondent of the German broadsheet Die Welt, Deniz Yücel, has been detained on charges of propaganda in support of a terrorist organisation since February. "We have no other choice - because we are responsible for the protection of the citizens of our country - but to adapt our travel and safety advisory to Turkey and let Germans know what can happen to them when they travel to Turkey".
Several weeks ago, Erdogan told Die Zeit weekly that if more German tourists shun the popular holiday destination, Turkey would simply seek to attract more visitors from Russian Federation, now the number two country of origin.
He also said Berlin could no longer guarantee German corporate investment in Turkey and issued new travel advice warning of risks to German citizens there.
In June, authorities detained Amnesty's local board chairman, Taner Kilic, along with 22 other lawyers, also for suspected links to Gulen, who has condemned the coup attempt and denied any involvement.
The list includes industry giants Daimler and BASF.
Germany was Turkey's top export destination in 2016, buying $14bn worth of Turkish goods. It was also the second-biggest source of Turkish imports, at US$21.5 billion.