President Volodymyr Zelensky has said everyone who commits atrocities against Ukraine’s civilians will be punished.
He said Ukrainians would not forgive or forget, and accused invading Russian troops of deliberate murder.
“There will be no quiet place on Earth for you. Except for the grave,” the president said.
Ukrainian officials say Russia is striking civilian targets around the country, including hospitals, nurseries, and schools.
But Russia denies targeting civilians, saying it is carrying out a “special military operation” against Ukrainian “nationalists” and “neo-Nazis”.
Ukraine’s Deputy Prime Minister Olha Stefanishyna told the BBC that, after “strong resistance” from the Ukrainian army, there was an “enormous operation” by Russia against civilians.
On Sunday alone, a family of four were killed when Russian forces fired shells at people fleeing the conflict in the town of Irpin, north-west of Kyiv.
And in the port city of Mariupol, promised evacuations were cancelled on both Saturday and Sunday amid fresh attacks.
The city council there said Russian shelling had made safe movement impossible. Russia has blamed Ukrainian forces.
The city is now in its sixth day with no running water, no power, and no sanitation. Food and water are fast running out.
Moscow announced it would open new evacuation corridors at 09:00 local time (07:00 GMT) in Mariupol and other cities. However, the routes published by Russia’s RIA Novosti news agency show some of the corridors end in Russia and Belarus.
The corridor from Kyiv will lead to Russian ally Belarus, and civilians from Kharkiv will only have a corridor leading to Russia.