Fifty-two people including five children were killed in a rocket attack on a train station in the eastern Ukrainian city of Kramatorsk. The city is being used for civilian evacuations, according to Donetsk region Governor Pavlo Kyrylenko.
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Ukrainian President Volodymyr Zelensky described Russia as an "evil with no limits" after the attack and called for a "firm global response".
US President Joe Biden accused Russia of being behind the attack, calling it a "horrific atrocity", while French Foreign Minister Jean-Yves Le Drian deemed it a "crime against humanity".
Russia's Defence Ministry accused Kyiv of carrying out the attack, saying it wanted to use fleeing residents "as a human shield to defend the positions of Ukraine's armed forces".
European Commission President Ursula von der Leyen said Russia will descend into "economic, financial and technological decay, while Ukraine is marching towards a European future", speaking after meeting Mr Zelensky in Kyiv.
Ukraine's southern city of Odessa imposed a curfew from Saturday evening to Monday evening over a "missile strike threat" from Russia, and after the shelling of the train station in Kramatorsk.
Civilians in eastern Ukraine are struggling to evacuate, after officials told them they have a "last chance" to avoid a major Russian offensive expected in the Donbas region.
Russia has redeployed its troops towards the east and south, aiming to create a land link between occupied Crimea and the Moscow-backed separatist regions of Donetsk and Lugansk in Donbas.
Ukrainian forces are in control of the northeast region of Sumy along the border with Russia, Governor Dmytro Zhyvytsky said on social media. "The region is not safe. There are many areas that have been mined and are still not cleared," he warned.
Russia said it is shutting down the local offices of a number of international organisations including Human Rights Watch, Amnesty International and the Carnegie Endowment for International Peace.
Britain also announced sanctions on the daughters of Russian President Vladimir Putin and Foreign Minister Sergey Lavrov, and sent Ukraine more "high-grade military equipment" including Starstreak anti-aircraft missiles and 800 anti-tank missiles.