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2 year oldResidential and administrative buildings in central areas of the city were damaged in the blasts.
Ukrainian President Volodymyr Zelensky said there were no military facilities in the area.
Kherson, the only regional capital captured by Russia since the invasion, was liberated by Ukraine last month.
Since then it has been frequently targeted by Russian forces positioned on the other side of the Dnipro river.
Videos from the aftermath of the attack show several bodies on the ground, cars in flames and damaged buildings.
It comes exactly 10 months since the beginning of the invasion.
Mr Zelensky wrote in his Telegram channel: "Social networks will most likely mark these photos as 'sensitive content'. But this is not sensitive content - it is the real life of Ukraine and Ukrainians."
He described the attacks as "killing for the sake of intimidation and pleasure".
Russia has frequently denied targeting civilians in its attacks.
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