Kiev, Ukraine (CNN) -- A new U.N. report shows an "alarming deterioration" of human rights in eastern Ukraine, the U.N. high commissioner for human rights, Navi Pillay, said Friday.
The report paints a troubling picture of the situation in Ukraine's east, citing cases of targeted killings, torture, beatings, abductions and sexual harassment, as well as intimidation of the media.
While many peaceful rallies take place in Ukraine, the findings show "an increasing tendency in some critical urban areas for rallies of opposing groups to be held simultaneously, often leading to violent confrontations," according to a statement from Pillay's office.
The 36-page report also notes "repeated acts of violence against peaceful participants of rallies, mainly those in support of Ukraine's unity and against the lawlessness in the cities and villages in eastern Ukraine."
"In most cases, local police did nothing to prevent violence, while in some cases it openly cooperated with the attackers," it states.
The report, compiled by 34 United Nations monitors on the ground, covers the period from April 2 to May 6.
Unrest in the region has increasingly flared into violence in recent weeks, as pro-Russian separatists clash with rival groups and Ukrainian security forces.
Pillay urged "those with influence on the armed groups responsible for much of the violence in eastern Ukraine to do their utmost to rein in these men who seem bent on tearing the country apart."
The report also highlights the issue of missing persons, including 83 still unaccounted for who vanished during the street protests in Kiev that led to the February ouster of pro-Moscow President Viktor Yanukovych.
While some of those who were abducted have been released, the bodies of others have been found dumped in rivers or elsewhere, particularly near Slovyansk in the Donetsk region, the statement said, with a local militia group "heavily implicated."
Accusations of killings and forced disappearances have also been made against state security services, the statement said.
Report: Crimean Tatars face problems
U.N. monitors in Ukraine also report serious problems emerging in Crimea, Pillay said, especially in relation to the minority Crimean Tatar population.
Ukraine's southeastern Crimea region was annexed by Russia in March after a controversial referendum.
Russian speakers make up a majority of the Black Sea peninsula's residents, but about 12% are Crimean Tatar, a predominately Muslim minority that was oppressed during the Soviet era.
Since the annexation, the U.N. monitors say, the Tatars have faced harassment if they did not meet a deadline to apply for Russian citizenship.
The report also notes curbs on the freedom of movement of Tatar leaders, cases of physical harassment, restrictions on Tatar media and fears that practicing Muslims will be persecuted.
Crimean leader Sergei Aksenov this week banned demonstrations in the region, only days ahead of a planned rally by Tatars to mark the 70th anniversary of the deportation of ethnic Tatars from Crimea under Josef Stalin.
Aksenov posted a message on his Facebook page saying no demonstrations would be allowed in the peninsula until June 6 in the interest of preventing extremism.
Tatars were forced out en masse on May 18, 1944 and only allowed to return to Crimea after Stalin died.
Russia's Foreign Ministry dismissed the findings of the U.N. report in a statement Friday.
"The U.N. report has little to do with the real situation related to the human rights in Ukraine," it said. "The complete lack of objectivity, total inconsistencies and double standards (of the report) don't leave any suspicion in that its authors are carrying out a political order to 'whitewash' the self-proclaimed authorities in Kiev."
Kiev and the West have condemned the annexation of Crimea and accuse Moscow of backing the pro-Russian militants in Ukraine's east. Moscow blames the unrest in Ukraine on far-right ultranationalist groups.
Billionaire opposes split from Ukraine
Pro-Russian activists in the eastern regions of Donetsk and Luhansk staged their own referendum on independence last weekend, which was condemned as illegitimate by Kiev and the West.
One of the richest men in the world, Donetsk-based steel and iron ore billionaire Rinat Akhmetov, took his own public stand against the separatists in a video message Wednesday.
Akhmetov said he favored a decentralization of power under a new constitution in Ukraine, but opposed his region joining Russia or trying to remain an independent "Donetsk People's Republic."
Either scenario, he said, would result in sanctions, and a loss of jobs and industry.
"We will come under huge sanctions, we will not sell our products, cannot produce. This means the stopping of factories, this means unemployment, this means poverty," he said.
Forbes magazine lists Akhmetov as the 92nd richest man in the world, worth $12.2 billion.
On Thursday, representatives of two of his factories in the restive eastern Ukrainian city of Mariupol co-signed a memorandum calling for public order and security after armed conflict in the city on May 9.
Ideological differences are not a reason for bloodshed, the declaration says. It calls for the disarming of the militias that have sprung up in Mariupol, as well as urging the government in Kiev to dismantle roadblocks into the city.
The city police, trade unions, NGOs, and a local representative of the self-declared Donetsk People's Republic were among those who signed the memorandum.
However, the self-declared Donetsk People's Republic distanced itself Friday from the document, saying on Twitter that "the government of the DPR did not sign the memorandum."
Steelworkers from Akhmetov's factories also have joined local police and representatives of the Donetsk People's Republic on joint patrols in Mariupol, local journalists and a spokeswoman for pro-Russian separatists in the city told CNN on Friday.
Irina Voropayeva, the spokeswoman, denied reports that the steelworkers themselves had removed barricades in the city, saying it was the separatists who had started it and the steelworkers joined in.
Ukraine's interim government, which took power after Yanukovych fled to Russia in February, is looking at constitutional reforms ahead of presidential elections scheduled for May 25.
CNN's Richard Allen Greene and Erin McLaughlin reported from Kiev, and Laura Smith-Spark wrote in London. CNN's Brian Walker, Boriana Milanova and Holly Yan contributed to this report, as did journalists Victoria Butenko, Lena Kashkarova and Azad Safanov in Kiev.