Contractors for the Wagner group have been deployed to numerous foreign wars, including in Ukraine and Syria.
Experts warned of risks if the Wagner paramilitary group succeeded in seizing control of Russia and gaining access to its nuclear warheads.
House Speaker Kevin McCarthy, R-CA, also claimed Putin is likely feeling vulnerable after the Wagner group's insurrection.
Russian President Vladimir Putin on Monday accused Ukraine and its Western allies of wanting Russians to "kill each other" during a revolt by mercenaries of the Wagner group, which stunned the country with an aborted march on Moscow over the weekend.
The two senators said the resolution sends a message to Russian President Vladimir Putin that NATO would respond if Russia uses nuclear weapons in Ukraine.
Experts say Putin's failure to keep Yevgeny Prigozhin in check makes Russia's power structure appear weak to Chinese President Xi Jinping.
Retired Deputy Commander of the 58th Combined Arms Army of the Southern Military District Andrey Gurulyov made the remarks on the "Evening with Vladimir Solovyov" show.
Wagner's Yevgeny Prigozhin previously accused the Russian military of bombing his war camps and killing his fighters in Ukraine.
Russia's crisis involving a mercenary group's aborted revolt against the Kremlin exposed "real cracks" in President Vladimir Putin's rule, US Secretary of State Antony Blinken said Sunday.
British military spies on Friday said Russia appears to be training combat dolphins in the annexed Crimean peninsula to counter Ukrainian forces.
Russian emergency services discovered a suicide note after they found Soviet Russian nuclear physicist and thermonuclear bomb creator Grigory Klinishov dead.
"If our tactical nuclear weapons give us an advantage, maybe it's time? Maybe we simply need to batter them," Russian TV presenter and propagandist Vladimir Solovyov said.
President Volodymyr Zelenskiy said on Thursday Ukrainian spies believe Russia was plotting an incident to release radiation from Europe's largest nuclear plant, an allegation denied by the Kremlin.
Members of the Ukrainian Navy SEALS saved four Russian soldiers trapped on the Dnipro River's left bank.
The Satan-2 nuclear warhead launcher can carry 10 multiple re-entry vehicles that can be sent to hit different targets.
Russia's constitutional court has rejected an attempt by rights groups to seek the repeal of a law that bans people from speaking out against Russia's invasion of Ukraine.
The transwoman was arrested after shouting "Glory to Ukraine" during a heated argument with a club guard.
Russia rewarded soldier Andrei Kravtsov at least one million rubles for destroying a Leopard tank.
President Joe Biden said the threat of Vladimir Putin using tactical nuclear weapons is "real," after Russia said it has begun delivering such weapons to Belarus.
"The Kyiv regime's planned flooding of Kherson region's territory may complicate the situation, including the situation with arbovirus infections," Russian official Igor Kirillov said.
The Baby Yoda pin was seen on Valerii Zaluzhnyii's flak jacket while he was discussing war plans with Lt. Gen. Serhiy Shaptala.
A Russian shell landed three meters away from the Ukrainian police officer and his son.