Russia's Feb 24 invasion of Ukraine has triggered the most serious crisis in relations between Russia and the West since the 1962 Cuban Missile Crisis, when many people feared the world was on the brink of nuclear war.
US President Joe Biden says Russian President Vladimir Putin is a war criminal and has led the West in arming Ukraine and imposing crippling sanctions on Russia.
"The idea of punishing a country that has one of the largest nuclear potentials is absurd. And potentially poses a threat to the existence of humanity," Medvedev, now deputy chairman of the Russian Security Council, said on Telegram on Wednesday.
Russia and the United States control about 90% of the world's nuclear warheads, with around 4,000 warheads each in their military stockpiles, according to the Federation of American Scientists.
Medvedev cast the United States as an empire which had spilled blood across the world, citing the killing of Native Americans, US nuclear attacks on Japan and a host of wars ranging from Vietnam to Afghanistan.
Attempts to use courts or tribunals to investigate Russia's actions in Ukraine would, Medvedev said, be futile and risk global devastation. Ukraine and its Western allies say Russian forces have engaged in war crimes.
Putin launched his invasion, calling it a "special military operation", to demilitarise Ukraine, root out what he said were dangerous nationalists and protect Russian speakers in that country.
Ukraine and its allies say Russia launched an imperial-style land grab, sparking the biggest conflict in Europe since World War Two.
After failing to seize the capital Kyiv early, Russia is now waging a war of attrition for Ukraine's Donbas region, parts of which are controlled by Russian separatist proxies.
On Sunday, Putin claimed his biggest victory when Ukrainian forces withdrew from Luhansk province. Russian forces then launched an offensive to take neighbouring Donetsk province. Donetsk and Luhansk comprise the Donbas.
Russia says it wants to wrest control of the eastern and heavily industrial region on behalf of Moscow-backed separatists in two self-proclaimed people’s republics.
On Wednesday, the Ukrainian military said it had so far staved off any major Russian advance into the north of Donetsk, but pressure is intensifying with heavy shelling on the city of Sloviansk and nearby populated areas.
It said Russian forces were bombarding several Ukrainian towns with heavy weaponry to enable ground forces to advance southward into the region and close in on Sloviansk.
"The enemy is trying to improve its tactical position...(They) advanced ... before being repulsed by our soldiers and retreating with losses," the Ukrainian military said in its evening note.
"We are holding back the enemy on the (Luhansk/Donetsk) border," Luhansk Governor Serhiy Gaidai told Ukrainian TV. Later, he said Luhansk was still not entirely occupied by Russian forces and that Russia had sustained "colossal losses."
"They will continue to try to advance on Sloviansk and Bakhmut. There is no doubt about that," he said.
Sloviansk Mayor Vadym Lyakh told a video briefing the city had been shelled for the last two weeks.
"The situation is tense," he said, adding that 17 residents had been killed there since Feb 24.
Russia's defence ministry says it does not target civilians and on Wednesday said it was using high-precision weapons to take out military threats.
Ukraine has repeatedly pleaded with the West to send more weapons to repel the invasion that has killed thousands, displaced millions, and flattened cities.
"At last, Western artillery has started to work powerfully, the weapons we are getting from our partners. And their accuracy is exactly what is needed," Ukrainian President Volodymyr Zelensky said In his nightly video message.
'NO SAFE AREAS'
In the Donetsk city of Kramatorsk, which Russian forces are expected to try to capture in coming weeks, Ukrainian soldiers and a handful of civilians ran errands in green-painted cars and vans on Wednesday. Much of the population has left.
"It's almost deserted. It's spooky," said Oleksandr, a 64-year-old retired metal worker. He was unlikely to follow official advice to evacuate, he said, despite an increase in missile strikes.
"I'm not looking for death but if I encounter it it's better to be at home," he said.
Outside the Donbas, Ukraine's second largest city Kharkiv was being subjected to "constant" longer-range Russian shelling, Mayor Ihor Terekhov said on Ukrainian TV.
"Russia is trying to demoralise Kharkiv but it won't get anywhere," he said. Ukrainian defenders pushed Russian armoured forces well back from Kharkiv early in the war, and Terekhov said around 1 million residents remained there.
South of Kharkiv, the governor of Dnipropetrovsk said the region had been battered by missiles and shelling, while on the southern coast the port of Mykolaiv was also being heavily shelled, Oleksandr Senkevych, its mayor, told a briefing.
"There are no safe areas in Mykolaiv," he said. "I am telling the people... that they need to leave."
Reuters was unable to immediately verify battlefield reports.