German Chancellor Angela Merkel rejected Ankara's accusations that her government had a hand in scrapping the rallies in two German towns in support of Erdogan's bid.
Turks vote April 16 on whether to create a presidential system that Ankara says will ensure political stability, but which critics argue will herald one-man rule by Erdogan, Turkey's strongman leader.
Ahead of the referendum, Turkish politicians' trips to Germany have sparked controversy, notably a rally by Prime Minister Binali Yildirim in the western city of Oberhausen to garner support for a "Yes" vote.
And on Thursday, several local authorities blocked rallies by two more Turkish ministers, prompting a furious response from Ankara which promptly summoned the German envoy to protest.
"They don't want Turkey to campaign here, they are working for a 'No'," Foreign Minister Mevlut Cavusoglu told reporters in the Turkish capital on Friday.
"They want to get in the way of a strong Turkey."
But the German government denied having anything to do with the municipal decision to block the rallies.
"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.
Bomb threat
Merkel said the decisions were "taken by municipalities, and as a matter of principle, we apply freedom of expression in Germany".
Vienna has also said it would not allow any campaign-related events.
The Turkish and German foreign ministers have spoken by phone, a senior Turkish official said without giving further detail.
As the political fallout continued, the western German town of Gaggenau which cancelled a rally by Turkish Justice Minister Bekir Bozdag said it received a bomb threat early Friday.
"The caller cited the cancellation of the event with the Turkish justice minister as a reason," local official Dieter Spannagel told AFP.
Bozdag had been due to meet the Turkish community there on Thursday, 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.
"Even if they don't allow (it), I will go from house-to-house to meet with our citizens in Germany," he was quoted as saying by the state-run Anadolu news agency.
Cavusoglu accused German officials of failing to "honour democracy" and of allowing "terrorists" from the outlawed Kurdistan Workers' Party to speak but denying the same right to Erdogan.
In response, a spokeswoman for Merkel said permits for rallies were only issued by local authorities and that freedom of opinion should be valued by both countries.
"The referendum is a domestic issue for Turkey," Ulrike Demmer said, adding: "Freedom of opinion ... should be respected" both in Turkey and in Germany.
'Learn how to behave'
Tensions have erupted previously over German criticism of the crackdown in Turkey following last year's failed coup, which has seen more than 100,000 people arrested, dismissed or sacked for alleged links to the plotters or to Kurdish militants.
Tempers on Monday flared again after 43-year-old Deniz Yucel, a correspondent for Germany's Die Welt daily, was charged by an Istanbul court with spreading terrorist propaganda and inciting hatred.
A dual national, he has been held in prison since February 18, with Germany's Vice Chancellor Sigmar Gabriel saying the case would make "everything harder" for Turkish-German relations.
After Thursday's developments, an irate Cavusoglu warned Germany, which is facing elections later this year, it would "need to learn how to behave towards Turkey" if Berlin wanted to maintain ties.
Merkel defended Germany's criticism over media freedom.
"I also think that it was right of us to criticise any restrictions on press freedom," she stressed.
But the German foreign ministry spokesman called for calm.
"It's in no one's interest... to cut off dialogue, to talk only through the media or to fall into open confrontation," Schaefer said.
Germany is home to the biggest 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.
burs-raz/fo/jm
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