"A collective EU response to prevent such campaign events would make sense so that individual countries like Germany where appearances are forbidden don't end up being pressured by Turkey," Kern told German newspaper Welt am Sonntag.
Ankara is wooing voters among Germany's three-million-strong population of Turkish origin - the largest outside Turkey -- to support expanding President Recep Tayyip Erdogan's powers in an April 16 referendum.
Several German towns prevented appearances by Erdogan's ministers last week, citing security and safety concerns.
The cancellations have angered the Turkish government, which accused Berlin of seeking to undermine its referendum campaign.
Defying local authorities' block on a referendum rally, economy minister Nihat Zeybekci is to speak Sunday at two private events organised by Turkish groups in Cologne and nearby Leverkusen.
Chancellor Angela Merkel on Saturday called Turkish Prime Minister Binali Yildirim to smooth the troubled waters, and the two countries' foreign ministers are set to meet later this week.
Berlin would "certainly not end our criticism of developments in Turkey, "German foreign minister Sigmar Gabriel said Sunday in a guest article for newspaper Bild am Sonntag.
Gabriel insisted Germany would stand up for the rule of law, freedom of opinion, human rights and democracy.
And he rejected Turkey's arrest of Die Welt newspaper journalist Deniz Yucel last Monday on terror charges as "wrong and disproportionate".
But "along with all the necessary criticism, we won't fall for those who want to vent their political spleen on Turkish-German relations," Gabriel went on.
"The German-Turkish friendship is deeper than the diplomatic tensions we're living through now."
Austrian leader Kern told the Welt am Sonntag that long-running EU accession negotiations with Turkey should be abandoned in response to Erdogan's "trampling on human rights and basic democratic rights".
"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.
"Introducing a presidential system will further weaken the rule of law in Turkey, reduce the division of powers and contradict the values of the EU."