"One cannot seriously comment on such misplaced statements," Merkel said at an event in Berlin, the dpa news agency reported.
Diplomatic tensions have been rising in recent days amid Turkish plans to have government ministers address rallies in Germany and the Netherlands in support of a national referendum on constitutional reform that would give Erdogan more powers.
Last week, local authorities in southwestern Germany withdrew permission for Turkey's justice minister to use a venue to hold a "yes" rally aimed at Turks living in Germany.
Merkel spokesman Steffen Seibert said earlier today that the German government "strongly rejected" that, adding that such comparisons downplay the crimes of the Nazis.
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Seibert noted that there are strong social, economic and military ties between Germany and Turkey, but acknowledged that there are "far-reaching differences of opinion" between Berlin and Ankara at the moment.
Seibert dismissed any notion that the federal government was involved in the decision to cancel events with Turkish officials, saying it was up to local officials to decide whether they could guarantee the necessary security.
However, Erdogan has several times threatened to quit the deal when expressing anger over European countries. Germany also has reconnaissance aircraft deployed at a NATO base in Turkey as part of the alliance's fight against the Islamic State group.
German Foreign Minister Sigmar Gabriel sought to smooth stirred-up emotions today and stressed the need to "normalize" what he calls a "highly strained" relationship with Turkey.
He also pointed out that EU countries have a common interest in not letting NATO partner Turkey "drift further to the east" and that German authorities back freedom of expression and that it's normal for Turkish politicians to want to address their compatriots in Germany, 1.4 million of whom are eligible to vote in the referendum.
"Our Austrian solution should be clear: we will not accept any campaign appearances by Turkish politicians in Austria," Austrian Foreign Minister Sebastian Kurz said as he arrived at a meeting of European Union counterparts in Brussels.
He added that "we don't want campaigns from other states to be brought to Austria and conflicts from other countries imported ... That is always damaging for integration.