Mercenary boss Prigozhin stopped short of calling on Russians to protest but urged everyone from "driver" to "flight attendant" to help him.
"If every Russian at his own level, in order not to call anyone to rallies, would simply say 'give ammunition to Wagner', as is already going on on social media, then this would already be important," he said on Telegram on Wednesday.
"We'll make them give (us) ammunition."
He had already made headlines on Tuesday when he accused Russia's top brass of essentially committing "treason."
After years operating in the shadows, the 61-year-old ally of Russian President Vladimir Putin has in recent months basked in the spotlight as his fighters spearhead the assault for cities in eastern Ukraine.
Prigozhin, who has recruited from prisons across Russia to bolster Wagner's ranks, has criticised Russia's regular army in Ukraine and recently slammed Moscow's "monstrous bureaucracy" for slowing military gains.
The months-long battle for the city of Bakhmut in eastern Ukraine has exposed tensions between Wagner and the regular forces.
On Tuesday, Prigozhin accused Defense Minister Sergei Shoigu and Chief of the General Staff Valery Gerasimov of refusing to supply his fighters with ammunition, saying that amounted to "treason".
Prigozhin accused the military command of having even prohibited the delivery to Wagner fighters of "shovels which allow them to dig trenches".
He has also accused the Russian military of attempting to "steal" victories from Wagner.