German Chancellor Angela Merkel rejected Turkey's bitter accusations that her government had had a hand in scrapping the rallies.
Turks vote on April 16 on whether to create a presidential system -- a change that the government says will ensure political stability, but which critics say will herald one-man rule by Erdogan.
In the runup to the referendum, controversy has flared over politicians' trips to Germany, where they have been seeking "Yes" votes from the millions of people of Turkish descent.
Yesterday, local authorities blocked rallies by two more Turkish ministers, prompting a furious response from Ankara which promptly summoned the German envoy to protest.
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"They don't want Turkey to campaign here, they are working for a 'No'," Foreign Minister Mevlut Cavusoglu told reporters in the Turkish capital today.
"They want to get in the way of a strong Turkey."
But the German government denied having had anything to do with the cancellations.
"That is a decision the federal government has absolutely no influence on... Because it falls under local or state jurisdiction on which we have zero influence," said foreign ministry spokesman Martin Schaefer.
Austria has also said it would not allow any campaign-related events.
Cavusoglu and German Foreign Minister Sigmar Gabriel, speaking by phone, agreed to meet next Wednesday, a senior Turkish official said.
As the political fallout continued today, a third German town -- Frechen, on the outskirts of Cologne, scrapped a rally that had been scheduled for Sunday, as the venue "excludes political events," police said.
And the western town of Gaggenau, which had scrapped a rally scheduled for yesterday by Turkish Justice Minister Bekir Bozdag, said it received a bomb threat early today.
Bozdag had been due to meet the Turkish community there yesterday, but cancelled his address after the Gaggenau authorities withdrew their consent for the Union of European Turkish Democrats (UETD) to use the hall, citing capacity problems.
Cologne city authorities also withdrew permission for the UETD to use a hall on Sunday for a speech by Economy Minister Nihat Zeybekci. But Zeybekci said he would still go ahead with the visit.