Germany is home to the largest population of Turks outside Turkey with around three million in the country of Turkish origin, the legacy of a massive "guest worker" programme in the 1960s-70s.
The row follows a decision by regional German officials to withdraw permission for rallies, in Gaggenau and Cologne, at which members of Mr Erdogan's cabinet were expected to urge the Turkish community to vote for constitutional changes giving Mr Erdogan sweeping new powers.
Several German towns prevented appearances by Erdogan's ministers last week, citing security and safety concerns.
Erdogan lashed out at Germany and accused Berlin of harboring him for a month at the German Consulate in Istanbul before agreeing to hand him over to authorities.
Speaking during an event in Istanbul on Sunday, Mr Erdogan said: "The Germans aren't letting our friends [ministers] talk.Well Germany, you're no democracy, you're not even close". The German government press office didn't immediately respond to calls seeking comment.
One attendee, Zehra Ferahtay, said the approval of constitutional changes would unify Turkey especially after the failed coup attempt last July to oust Erdogan's government.
"I believe that you are holding the key to victory" in the coming vote, Erdogan said. Mass arrests and dismissals in professions from the military to academia, journalism to science, have been heavily criticised in the West.
"We will go where we want to go, we will meet with our citizens and we will have our meetings", said Cavusoglu in response to Rutte's post.
"We can't continue negotiating about membership with a country that has been distancing itself from democratic norms and rule-of-law principles for years", Kern said.
The row over Turkish ministers holding political rallies in some European Union countries has intensified, with the Turkish President making a Nazi comparison in criticising German bans on the meetings.
Stephan Meyer, interor affairs spokesman for Merkel's Bavarian allies, the Christian Social Union (CSU), said the "export" of Turkey's internal conflict to Germany should "not be tolerated". The deputy leader of Chancellor Angela Merkel's Christian Democratic Union (CDU) party said the Turkish president was "reacting like a wilful child that can not have his way", while a top leader of the CDU's Bavarian sister party described Erdogan as the "despot of the Bosphorus" and demanded an apology.