The women have accused Putin of "hiding" from the mothers and wives of Russian soldiers sent to fight in Ukraine.
Ahead of a planned meeting between the president and conscripts' families, one mother and campaigner asked whether Putin had the courage to talk to "women who aren't in your pocket."
"The newly mobilized...have not yet been taught how to properly disguise themselves," said Serhiy Cherevaty, a spokesman for Ukraine's armed forces.
The Russian president is facing mounting opposition to his war against Ukraine from the mothers of his country's soldiers.
Many are voicing their dissatisfaction with Vladimir Putin's partial mobilization order.
Russian President Vladimir Putin already announced on November 3 that he would pay mobilized soldiers 195,000 rubles ($3,237) per month.
"We aren't seeing results," a guest on Russian state TV said following retreat from the city of Kherson.
Russia recently withdrew its forces from the strategically important city of Kherson in southern Ukraine.
Tigran Keosayan said napalm could be used against NATO troops.
Alexander Dugin shared a veiled threat to Vladimir Putin that hinted he could be replaced.
Footage shows soldiers being greeted by those celebrating the Russian withdrawal from the southern Ukrainian city.
Ukraine's armed forces described "strained" relations between drafted troops and those from the Russian republic.
Russian officials have portrayed the withdrawal as part of its military strategy.
Amid Ukraine's gains in Kherson, a U.S. think tank warns that a winter ceasefire would only help Russia.
Many of those casualties came from Bakhmut, an area in eastern Ukraine under heavy fire from Russian forces.
Ukraine's Ministry of Defense published a video that appears to show Ukrainian attacks on Russian columns retreating across the Dnieper River.
Mobilized soldiers only have about 100 rounds of ammunition for 20 to 30 people, one woman claimed.
The far-right Rusich group criticized the retreat from the southern Ukrainian city on Telegram in a message aimed at "the clowns from the Moscow Region."
"Deserters who abandoned the combat order and betrayed their comrades" should face the death penalty, said Kremlin propagandist Vladimir Solovyov.
"I'm ready to tear them apart. They have to do something...we want them to be taken out as they have a lot of wounded," one woman said.
Sergey Surovikin, head of Russia's forces, said troops would be retreating to "preserve the lives of our soldiers and the combat capability of the troop group."
Students will learn combat training, the basics of shooting, and the use and construction of hand grenades, among other skills, a Russian official said.
His wife said his mobilization may be the revenge of the local "elites," according to local media sources.
"When it all started, the officers immediately ran away," a soldier who was conscripted as part of Russian President Vladimir Putin's partial mobilization said.
He also suggested younger men should be sent into battle as the government would not need to pay widows and children should they die.
It comes after reports that Colonel General Alexander Lapin had been fired from his role as commander of Russia's Central Military District in late October.
The Ukrainian Air Force's South Command said three Russian ammunition depots in the Beryslav and Kherson district had also been destroyed.
Boris Bondarev said he thought Putin knew the "Russian army is not as strong as it is reported to be."
Colonel General Alexander Lapin reportedly threatened to shoot the commander of a mobilized unit which retreated from the front lines.
The general has come under fire recently from Chechen leader Ramzan Kadyrov and Yevgeny Prigozhin, founder of the Wagner Group, a Russian mercenary outfit.