The governor of Ohio, Mike DeWine, has issued a statement condemning hate speech at a protest against his state’s anti-coronavirus measures – as well as a Republican state senator who compared the state’s department of health to Nazi Germany.

Posting on Twitter, Mr DeWine “I am deeply concerned by the anti-Semitic sign at Ohio’s Statehouse during a recent protest rally, he wrote. “The sign was vile and disgusting. While even disgusting speech is constitutionally protected, it still demands condemnation.”

The sign in question was a mocked-up Israeli flag, featuring a blue rat stamped with a white star of David and the words “the real plague”.

It was displayed at a rally outside the statehouse in Columbus, one of a number of similar protests across the US in which crowds – most of them relatively small – have descended on state capitals to demand an end to lockdown policies, in some cities blocking traffic and waving pro-Trump signs. One such protest in Olympia, Washington featured speakers from far-right movements.

Away from the streets of Columbus on Facebook, also indulging in anti-semitic propaganda were an Ohio state senator, Andrew Brenner, and his wife, both of whom felt Mr DeWine’s anger as well.

“The recent internet post by Ohio State Senator Andrew Brenner, likening Ohio’s Department of Health Director’s actions to fight coronavirus to those taken by the Nazis in Germany during World War II, must also be condemned.”

Mr Brenner had posted a reply to a defiant message his wife, Sara Marie, posted on Facebook on Tuesday, in which she said:

“With a German accent, in your head say ‘Show me your papers’. You don’t issue people certificates to be able to function outside of their home. You don’t issue people a certificate to allow them to go to work. This is mark of the beast type talk.

“This is worse than China, for heaven’s sake. This actually feels like Hitler’s Germany where you had to have blond hair and blue eyes to be able to function anywhere, and you were damned otherwise. When are people going to say enough is enough?”

Mr Brenner replied: “We won’t allow that to happen in Ohio.”

Ms Brenner also posted a picture of a concentration camp, superimposed with the message: “If people were told to get in cattle cars to be taken to virus protection camps, most of you would rush to get in line …”

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The posts have now been deleted – but having seen them, Mr DeWine was unambiguous in his response.

“The comments showed a complete lack of understanding of the Holocaust – made even more offensive by posting on Holocaust Memorial Day – and was a slur on a good, compassionate, and honorable person who has worked non-stop to save lives and protect her fellow citizens.”

“Any complaints about the policy of this administration need to be directed at me. I am the office holder, and I appointed the Director. Ultimately, I am responsible for the decisions in regard to the coronavirus. The buck stops with me.”