He added: "If Republicans were doing that, they'd be warming up the gas chamber right now."
A spokesman for Clinton's campaign tweeted the comments Thursday morning, agreeing with a reporter who labeled them a Holocaust joke.
Update: Now Clinton herself has retweeted fellow presidential candidate Evan McMullin, who called it a "Nazi reference."
This is hardly the first time allegations of anti-Semitism have crept into the 2016 campaign.
The Trump campaign has previously found itself under fire for using imagery that could be construed as anti-Semitic. In July, Trump tweeted an image with a six-pointed star around the words "Most Corrupt Candidate Ever!" Next to the star was a picture of Clinton's face. In the background was a layer of hundred-dollar bills.
The image was taken from a Twitter user who disparaged Muslims, black Democrats and others, yet the Trump campaign argued that the whole thing was being blown out of proportion. As I wrote at the time:
The problem with the original tweet wasn't that the use of a six-pointed star is inherently anti-Semitic. The problem was what else was contained in the tweet with the six-pointed star — the words "Most Corrupt Candidate Ever!" — and that the star was overlaid on top of a bunch of money. This brings to bear some of the most well-established stereotypes and racist beliefs about Jewish people and money.
Last month, a Trump foreign policy adviser was accused of making anti-Semitic comments. And throughout the campaign, Jewish reporters have been harassed by Trump supporters who espouse anti-Semitic ideas.
The Trump campaign has offered the formulation that Donald Trump Jr. used before, but with the electric chair subbed in for the gas chamber. After former Mexican president Vicente Fox criticized Trump by using a vulgarity, Trump again suggested that the media would kill him for doing such a thing.
"Can you imagine if I used the F-bomb?" Trump said. "It would be the electric chair, right?"
As with all things Trump, Trump Jr.'s comments are questionable enough to cause controversy but oblique enough that defenders claim they had nothing to do with the Holocaust.
Update: The Trump campaign responds: