Russia must face "just punishment" over its invasion of Ukraine, President Volodymyr Zelensky has told the UN General Assembly in New York.
In a pre-recorded video, the Ukrainian leader called for the creation of a special war tribunal and detailed alleged war crimes by Russia.
He also set out a "formula", including more military support and to punish Russia on the world stage.
Russia's Vladimir Putin had earlier called up 300,000 reservists for duty.
The move prompted rare protests in dozens of Russian cities and Mr Zelensky said the partial mobilisation showed his enemy was not serious about peace talks. Monitoring group OVD-Info said 1,315 Russians had been arrested.
The Kremlin said the call-up would be limited to those who had completed military service and had important skills and combat experience. But some of those arrested during protests in Moscow were also told they would have to sign up, reports say.
The Ukrainian leader said creating a special tribunal would help hold Moscow to account for stealing territory and murdering thousands of people. His address on Wednesday received a standing ovation from many of the session's attendees.
Despite Russia's decision to bolster its military campaign, the two sides took part in the biggest exchange of prisoners since the start of the war.
In a deal brokered by Saudi Arabia, 215 fighters were returned to the Ukrainian side, including 10 foreigners - while Russia took back 55 soldiers. Pro-Russian politician Viktor Medvechuk was also part of the swap. He has been seen as President Putin's closest ally in Ukraine and faced treason charges.
Ukraine said that among those released were 108 members of the Azov battalion who for weeks defied Russia's bombardment of Mariupol and the city's steel plant.
Battalion commander Denys Prokopenko and his deputy were among five senior officers freed. So too was Ukrainian military medic Mariana Mamonova, who is more than eight months pregnant and was being held in the notorious Olenivka prison in an area of eastern Ukraine held by Russian-backed separatists.
A fellow prisoner, who was released in July, told the BBC how the medic was forced to live in a cell with several other people, sleeping on the floor and going outside only once a day. Her husband had feared their baby would be taken away.
Ten foreign prisoners held by Russian-backed forces were also released, including five British nationals and two Americans.
In his UN address, Mr Zelensky condemned Russian plans to stage so-called referendums on joining Russia in occupied areas of Ukraine. The vote which is due to start on Friday has been widely condemned as a sham by Western leaders.
He addressed the discovery of 445 new graves in Izyum, a north-eastern city recently retaken from Russian forces during a sweeping Ukrainian counter-offensive.
Mr Zelensky detailed allegations of war crimes in the city, including against one man said to have been castrated and murdered.
"Why are the Russian military so obsessed with castration?" he asked.
The word "punishment" cropped up some 15 times in Mr Zelensky's speech, and was the first of his five non-negotiable conditions for peace.
Russia must face consequences for its aggression, he said, through further sanctions and by the UN stripping Moscow of its powerful role as a permanent Security Council member.
He also called for Ukrainian lives to be protected, and for the country's internationally-recognised borders to be respected.
As his fourth and fifth conditions, he called for new security guarantees for Kyiv, and for the world to unite in calling out Moscow's armed aggression.
Later on Wednesday, the European Union's foreign policy chief said EU countries had agreed to hit Russia with new sanctions.
Josep Borrell told reporters the new restrictions would target Russian individuals and the country's economic sectors.
Sporting his signature green T-shirt in his video, Mr Zelensky thanked the 101 countries at the UN which voted to allow him to address the assembly in a video rather than in person.
He blasted the seven countries including Russia which voted against his video appearance, and criticised those which have remained neutral during the conflict.