In a speech in Gumushane, northern Turkey, Erdogan made references to members of the movement led by Fethullah Gulen, living in exile in the United States whom Ankara blames for a coup attempt in 2016, but did not directly mention the US or Trump.
"Those who did not take a single step over the coward [members of the Gulen movement], whom they cherished, hosted in mansions, cannot lecture us on law," he said. "They cannot use the language of threat and blackmail against this nation. Bullying this nation will get them nowhere."
Erdogan also called for a solution through peaceful negotiations and diplomacy.
In announcing the tariffs on Twitter, Trump also took a shot at Turkey's currency crisis as the lira tumbles to record lows against the dollar and euro.
"I have just authorized a doubling of Tariffs on Steel and Aluminum with respect to Turkey as their currency, the Turkish Lira, slides rapidly downward against our very strong Dollar!" Trump wrote.
"Aluminum will now be 20% and Steel 50%. Our relations with Turkey are not good at this time!"
Trump had authorized the preparation of documents to raise tariffs on imports of steel and aluminum from Turkey, White House spokeswoman Lindsay Walters said.
The type of tariffs Trump referred can be imposed on imports from particular countries whose exports threaten to impair national security independent of negotiations on trade or any other matter, Walters' statement said.