Binali Yildirim also told the several thousands of people at a stadium in Oberhausen, in western Germany, that Turkey would track down the participants in last July's failed military coup "in all the holes where they are hiding".
Germany is home to about three million people of Turkish origin, the legacy of a massive "guest worker" programme in the 1960s and 70s and the biggest population of Turks in the world outside of Turkey.
Critics say the new presidential system will cement one-man rule in the country.
Some 750 opponents of Erdogan rallied peacefully near the Oberhausen stadium, according to police.
Sevim Dagdelen, a lawmaker in Germany's far-left Die Linke party, called the rally "a publicity campaign for a dictator".
Another lawmaker, Cem Ozdemir of the Greens, wrote in the Kolner Stadt Anzeiger paper: "I find it shocking that a Turkish prime minister has no qualms about taking advantage of our democracy while he and his henchmen make their opponents disappear behind bars," he said.
The German daily Die Welt said yesterday that Turkish police were holding its correspondent in the country.
Deniz Yucel, 43, has been detained in connection with reports on a hacker attack on the email account of Turkish Energy Minister Berat Albayrak, a son-in-law of Erdogan, the paper said.
Yildirim met Chancellor Angela Merkel earlier today during the Munich Security Conference, where she raised the correspondent's case.
Yildirim was to meet US Vice President Mike Pence at the conference later today.
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