According to Press TV, Cavusoglu said on Thursday that Germany was welcome to withdraw its troops from Incirlik Air Base in southern Turkey if it desired.
"If they want to leave, let's just say goodbye," he told Turkey’s broadcaster NTV, adding, "That's up to them and we won't beg."
Cavusoglu also aired a previous grievance over Germany's decision to prevent him and other Turkish ministers from holding rallies on German soil before Turkey's April 16 referendum on expanding presidential powers.
"If what we are doing is blackmail, then what was that?" he said.
He was responding to comments from German politicians, who have raised the prospect of withdrawing troops from the base in southern Turkey.
Turkey have prevented German lawmakers from visiting the country's soldiers at the base in response to Berlin's decision to grant asylum to Turkish soldiers accused of participating in last year's failed coup.
Germany has about 250 military personnel stationed there, flying Tornado surveillance missions over Syria and refueling flights for partner nations allegedly battling Daesh terrorists.
Foreign Minister Sigmar Gabriel in an interview with German newspaper Neue Osnabrucker Zeitung accused Ankara on Wednesday of "looking to blackmail" the German parliament.
"If it is not possible to work normally at Incirlik - and this includes visits by German parliament lawmakers - then we will have to look for alternatives," Gabriel said.
"I can only hope that the Turkish government will change its mind in the coming days. Otherwise, the parliament will no longer let our soldiers go to Turkey," he added.
