Political leaders have shunned the Alternative for Germany. But on his social media platform X, Mr. Musk is pitching the party as mainstream.

The publicity was a potential boon for AfD, which has been frozen out of mainstream politics, in part, because its leaders have downplayed Nazi atrocities.

Elon Musk strongly endorsed the far-right Alternative for Germany Thursday in a discussion with the party’s leader that was broadcast live on X — a potential violation of German law.