Family members mourn Vasyl Sushchuk, an Azov regiment serviceman killed during the Russian invasion of Ukraine, during his funeral. AFP
The Russian tweet came as Moscow and Kyiv traded blame over a strike on a jail holding Ukrainian prisoners of war in Russian-controlled territory that killed around 50 people, reportedly including members of the Azov regiment.
"Azov militants deserve execution, but death not by firing squad but by hanging, because they're not real soldiers. They deserve a humiliating death," Moscow's diplomatic mission wrote in an overnight Tweet.
The post -- which Twitter said violated its rules on "hateful conduct" -- was accompanied by a video purportedly showing a couple in Russian-held Mariupol claiming they had been shelled by Ukrainian forces at the Azovstal metal plant during the fierce battle for the city.
"Russia is a terrorist state. In the 21st century, only savages and terrorists can talk at the diplomatic level about the fact that people deserve to be executed by hanging. Russia is a state sponsor of terrorism," Andriy Yermak, head of the office of the Ukrainian presidency, wrote on Telegram.
"What more evidence is needed?"
Russia and Ukraine have accused each other of carrying out the deadly bombardment of the jail holding captured servicemen in Kremlin-controlled Olenivka.
Moscow said Ukraine targeted the facility in a bid to dissuade its troops from surrendering, while Kyiv accused Russia of carrying out a "war crime" by striking the prison.
Ukraine's foreign ministry spokesman Oleg Nikolenko tweeted "there is no difference between Russian diplomats calling for execution of Ukrainian prisoners of war and Russian troops doing it in Olenivka. They are all accomplices in these war crimes and must be held accountable."
Ukrainian forces, including members of Azov, in May ended a weeks-long siege of the vast Azovstal plant in Mariupol by agreeing to surrender.
Around 2,500 combatants were taken captive by Moscow's forces after calling a halt to their resistance.
Azov regiment commander Mykyta Nadtochiy said in a video address: "We consider the attack on Olenivka an act of public execution committed by Russia with complete impunity."
Those responsible for this act will be "found wherever they are" and Ukraine as a state "will ensure that they are punished justly," he added.
The Azov regiment is a former volunteer battalion that has drawn controversy for its links to far-right figures.
The group was formally incorporated into Ukraine's National Guard in 2014 as it helped fight Kremlin-backed separatists in east Ukraine.
Azov fighters are a hate figure for Russia's tightly-controlled state media and officials, who demonise them as "neo-nazis".
The Kremlin claims it launched its invasion of its pro-Western neighbour in February in part due to the need to "denazify" the country.
Kyiv and its Western allies have roundly rejected the claim and say it was used as a pretext to fuel support inside Russia for the assault on Ukraine.