At least 69 threats have been sent to almost 30 public figures and institutions across the country, said Peter Beuth, the interior minister of the state of Hesse.
The anonymous messages were all signed “NSU 2.0”, a reference to the German neo-Nazi cell National Socialist Underground that committed a string of racist murders in the 2000s.
Beuth told the Hesse state parliament that in three cases, the recipients' contact details may have been taken from police computers.
Last week, Hesse police chief Udo Muench resigned after it emerged that police computers were used to search for details of a far-left politician who subsequently received threatening emails.
On Tuesday, Beuth said there was so far “no proof” of a right-wing network within the police.
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He added that the state police force was working to “restore its integrity” and identify the sender.
The row entangling Hesse's police force came as German law enforcement services are under close scrutiny over far-right extremism in their midst.
Germany's defence minister last month ordered the partial dissolution of the elite KSK commando force over right-wing extremism.
While far-right extremism was once thought to plague mostly eastern states, Hesse was shaken last year by the murder of pro-migrant politician Walter Luebcke at the hands of a neo-Nazi.
It was also in a city in the region — Hanau — where a man gunned down nine people of foreign origin in February this year.