Days after Elon Musk set off a firestorm with an odd gesture that struck some as a Nazi salute, the billionaire entrepreneur drew criticism Thursday for a series of word puns using the names of Third Reich leaders.

“Don’t say Hess to Nazi accusations!” Mr. Musk wrote on his social media platform X among a handful of others that included, “Some people will Goebbels anything down!” and “His pronouns would’ve been He/Himmler! Bet you did nazi that coming.” He ended his post with a crying laughing emoji.

The CEO of the Anti-Defamation League (ADL), Jonathan Greenblatt, responded, “the Holocaust is not a joke.”

“We’ve said it hundreds of times before and we will say it again: the Holocaust was a singularly evil event, and it is inappropriate and offensive to make light of it,” Mr. Greenblatt wrote on X.

The official ADL social media account also blasted Mr. Musk, saying such jokes “trivialize the Holocaust” and “only serve to minimize the evil and inhumanity of Nazi crimes, denigrate the suffering of both victims and survivors and insult the memory of the six million Jews murdered in the Shoah.”

Ted Deutch, CEO of the American Jewish Committee, condemned Mr. Musk’s jokes. “Wordplay about Nazis isn’t funny. It isn’t clever. And it’s dangerous,” Mr. Deutch wrote on X. 

Addressing Mr. Musk, he added, “However you feel about the accusations being made against you, this is absolutely the wrong response. Nazi-themed ‘jokes’ are offensive and harmful. Don’t belittle the seriousness of the Holocaust; you give cover to those who seek to do the same.”

The ADL’s rebuttals to Musk, who has been active on Twitter to defend himself against those who accused him of performing a “Sieg Heil” salute while on stage at an inauguration event for Trump on Monday, stand in contrast with the organization defending him following the incident.

In that instance, the ADL said, “It seems that he made an awkward gesture in a moment of enthusiasm, not a Nazi salute.” The antisemitism watchdog wrote on X that Mr. Trump’s first day back in the White House was a “delicate moment” and that “many are on edge,” which the group said it “appreciates.” 

“Our politics are inflamed, and social media only adds to the anxiety,” the ADL said.  

Before the Nazi puns were posted, Israeli Prime Minister Benjamin Netanyahu on Thursday also defended Mr. Musk in regard to his hand gesture, calling him a “great friend of Israel.” Mr. Netanyahu said Mr. Musk is being “falsely smeared” and praised him as someone who has “repeatedly and forcefully supported Israel’s right to defend itself against genocidal terrorists and regimes who seek to annihilate the one and only Jewish state.”