"A Turkish campaign has no business being here in Germany," he told public broadcaster ARD yesterday, saying he is "strongly opposed politically" to such events.
Ankara is locked in a dispute with several European countries which have sought to stop Turkish ministers from holding rallies in their countries ahead of an April referendum aimed at expanding President Recep Tayyip Erdogan's powers.
German local authorities this month scrapped such campaign appearances over logistical problems, sparking an angry response from Ankara, which is keen to win votes from the Turkish diaspora.
De Maiziere said while he is opposed to such appearances, the question of whether to impose an outright entry ban requires careful consideration.
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"But there are limits -- clear limits, for example in the criminal code. It is hardly noticed," he said.
"Someone who insults and maliciously condemns Germany or its constitution has committed a criminal offence. That would at least be a limit," he said.
Erdogan had labelled the decision by German local authorities to halt the rallies as "Nazi practices", sparking consternation in Berlin.
But on any future rallies, she said: "We continue to view such appearances by Turkish government representatives as possible as long as they are duly announced, in a timely manner, and in an open way."
Separately, Finance Minister Wolfgang Schaeuble said he hoped Turkey "would return to its senses."
Through the dispute, as well as Ankara's arrest of a correspondent of German daily Die Welt, Schaeuble said: "Turkey and those responsible in Turkey have destroyed the basis for further progress in cooperation."
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