Comparisons with Nazi Germany are "lines that should not be crossed", the German foreign minister has warned his Turkish counterpart as they met to try to defuse a bitter row.
But Sigmar Gabriel also emphasised his wish to return to "friendly relations".
President Recep Tayyip Erdogan has accused Germany of "Nazi practices" because of the cancellation of rallies involving Turkish ministers.
He is seeking new constitutional powers in a 16 April referendum.
Foreign Minister Mevlut Cavusoglu repeated the Nazi comparison on a visit to Hamburg aimed at drumming up support among some of the 1.4 million Turkish voters who live in Germany.
The Dutch and Austrian governments have also criticised the Turkish government's drive to take its referendum campaign to Turks based in EU countries.
German Chancellor Angela Merkel has condemned the Nazi jibe as "unacceptable" and Mr Gabriel echoed her sentiment after a breakfast meeting in Berlin with Mr Cavusoglu.
But Mr Gabriel was also keen to stress the former "success" of the two nations' ties, and stressed his intention to avoid lasting damage to them.
Relations have deteriorated since last July's attempted coup in Turkey - with Germany critical of the mass arrests and purges that followed, while Turkey has bridled at its EU neighbours' perceived lack of support.
In the latest row, Mr Cavusoglu accused German authorities of "systematic pressure" on German-based Turks. He said Germany should not give Turkey "democracy and human rights lessons".
He was speaking from the balcony of Turkey's consular residence in Hamburg on Tuesday evening after the building originally scheduled for the rally was closed by authorities.
Mr Gabriel said such decisions were down to local authorities and often based on safety considerations.
Another contentious subject raised at Wednesday morning's meeting, according to Mr Gabriel, was the fate of Deniz Yucel, a German-Turkish journalist working for Die Welt who has been detained in Turkey for alleged terrorism propaganda.
Mr Cavusoglu agreed to give Germany consular access to the reporter, Mr Gabriel said.