The UN has warned of an "alarming deterioration" in human rights in eastern Ukraine, where separatists are fighting security forces.
It also found "serious problems" of harassment and persecution of ethnic Tatars in Crimea, the mainly ethnic Russian region Moscow annexed in March.
Russia condemned the report, saying it ignored abuses by Ukraine's government.
Meanwhile, a third-party initiative to restore law and order in one troubled city, Mariupol, seems to be succeeding.
Violence between separatists and pro-Ukrainian forces has left dozens dead in the east and south this month.
Separatists control towns in the Donetsk and Luhansk regions, where they have been skirmishing with units of the Ukrainian security forces, sent in to reassert government control.
The revolt in the east gained momentum after Russia annexed Ukraine's mainly ethnic Russian region of Crimea in March.
Moscow acted after the overthrow of Ukraine's elected pro-Russian President, Viktor Yanukovych, during unrest in the capital Kiev in February, and his replacement with an interim government, backed by Ukrainian nationalists. A new Ukrainian president is due to be elected on 25 May.
In another development, former German Chancellor Helmut Schmidt has accused EU officials of risking war with Russia by displaying "megalomania" in Ukraine.
Mr Schmidt, chancellor from 1974 to 1982, told German newspaper Bild: "The danger that the situation gets ever more tense, as it did in August 1914, is growing day by day."
'Tearing Ukraine apart'
The UN's conclusions are contained in a 37-page report, its second monthly assessment of the situation.
UN human rights chief Navi Pillay said in Geneva: "Those with influence on the armed groups responsible for much of the violence in eastern Ukraine [must] do their utmost to rein in these men who seem bent on tearing the country apart."
The UN's report details growing lawlessness in eastern and southern Ukraine:
- Peaceful demonstrations, primarily by supporters of Ukraine's unity, deteriorate into violence
- Protesters are attacked and beaten
- Local police do nothing to prevent the violence and sometimes openly co-operate with the attackers
UN monitors have also documented cases of targeted killings, torture and abduction, primarily carried out by anti-government forces in eastern Ukraine.
The report highlights threats to journalists and international observers, and abductions or attacks on some.
In its response, Russia's foreign ministry said the report lacked any semblance of objectivity, and accused its authors of following "political orders" to whitewash Ukraine's new, pro-Western leaders.
The report, it said in a statement in Russian, ignored "the crudest violations of human rights by the self-proclaimed Kiev authorities".
Separatists in Donetsk announced on Thursday they were setting up their own parliament and were planning to open the border with Russia shortly.
Steelworkers in the flash-point port of Mariupol have begun citizen patrols after talks between officials from their company Metinvest, which is owned by oligarch Rinat Akhmetov, and local police and community leaders.
Metinvest employees could be seen on Friday removing barricades in the city. There are conflicting reports as to whether separatists in the city are backing the initiative too.
Mr Akhmetov, Ukraine's richest man, was the main financial backer of deposed President Yanukovych and remains a powerful figure. He has called for the east to remain inside a "united Ukraine".
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