Erdogan, who was speaking at a meeting of an Islamic foundation in Istanbul, said the reporter, Deniz Yucel of Germany's Die Welt newspaper, would be tried by Turkey's independent judiciary.
The dispute, following political campaigning, to push for a constitutional referendum in Turkey intensified after cancellation of a rally to be led by Cavusoglu in Rotterdam on March 11.
Relations between Ankara and Berlin have been further upset following the arrest of a Turkish-German journalist in Ankara over his reports on Turkey's treatment of its Kurdish population.
He also warned Turkish politicians that they could be banned from holding rallies in Germany if they do not stick to German laws: "Whoever crosses these lines cannot expect to be allowed to propagate his political ideas here".
If Germany comes down hard on Turkey, it will surely strengthen Erdogan and bring dire consequences, Gabriel stressed, while not referring to the publication directly.
He told Der Spiegel that upcoming negotiations about the EU's future relationship with Britain might provide a blueprint for Turkey "in the long term".
Suleyman Soylu, Turkey's interior minister, threatened Thursday to "blow the mind" of Europe by sending 15,000 refugees per month to the European Union. "We have done everything for that and the Turkish people are fed up of waiting", he said, preferring to stay anonymous.
"The deal's goal isn't all that complex: Erdoğan, whose country is home to just under three million refugees, has agreed to prevent a further wave of migration to Germany and is being paid a handsome sum of money for his services as doorman".
Turkish authorities have blamed a rogue military group led by Mr Gulen for the attempted putsch that left 248 people dead.
The European Union (EU) heaped praise on the EU-Turkey deal in a factsheet published on Friday, a day ahead of its one-year anniversary, saying it remarkably reduced migratory flows from Turkey to Greece and the loss of life at the sea.
With less than seven months up to the parliamentary elections in Germany, critics say Merkel has been conspicuously submissive in her approach to Erdogan for fear of him scrapping the refugee deal and thus destroying chances of her reelection. As we documented, Erdogan already has purged academia and the media.