The UN has received 75 allegations of sexual violence by Russian forces, including against children.
Russian actions in Ukraine, which have included summary executions of civilians and levelling of civilian infrastructure, may amount to war crimes, the UN said on Friday.
"Our work to date has detailed a horror story of violations perpetrated against civilians," United Nations High Commissioner for Human Rights Michelle Bachelet said on Friday.
"Over these eight weeks, international humanitarian law has not merely been ignored but seemingly tossed aside," she said.
"Russian armed forces have indiscriminately shelled and bombed populated areas, killing civilians and wrecking hospitals, schools and other civilian infrastructure, actions that may amount to war crimes," said spokeswoman Ravina Shamdasani.
In the town of Bucha, near Kyiv, a UN rights monitoring mission has documented that 50 civilians had been killed there, including by summary execution, Shamdasani said.
"Almost every resident in Bucha our colleagues spoke to told us about the death of a relative, a neighbour or even a stranger. We know much more needs to be done to uncover what happened there and we also know Bucha is not an isolated incident," Bachelet said.
The UN mission has received more than 300 allegations of killings of civilians in areas around Kyiv, Chernihiv, Kharkiv and Sumy that were under Russian control until early March.
It "has also documented what appears to be the use of weapons with indiscriminate effects, causing civilian casualties and damage to civilian objects, by Ukrainian armed forces in the east of the country."
From the start of the war on February 24 to midnight on April 20, the UN mission has documented and verified 2,345 civilians have been killed and 2,919 wounded, it said.
"We know the actual numbers are going to be much higher as the horrors inflicted in areas of intense fighting, such as Mariupol, come to light," Bachelet said.
The UN has received 75 allegations of sexual violence by Russian forces, including against children.
"First and foremost, this senseless war must stop," Bachelet said.
"But as the fighting shows no sign of abating, it is vital that all parties to the conflict give clear instructions to their combatants to strictly respect international humanitarian law and international human rights law," she said.
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