The United Nations has warned of an "alarming deterioration" of human rights in eastern Ukraine, where the army is battling an insurgency by pro-Russian separatists.

In a new report, UN High Commissioner for Human Rights Navi Pillay also voiced deep concern about "serious problems" of harassment and persecution of the Tatar community in Crimea.

Crimea was annexed by Russia in March in the face of international outrage.

"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," Mr Pillay said in a statement.

The report catalogues a litany of "targeted killings, torture and beatings, abductions, intimidation and some cases of sexual harassment", which it said was carried out by anti-government groups in the east of Ukraine.

Kiev's interim leaders are waging a military offensive against pro-Moscow separatists, who took up arms against the central government after the ouster of the Kremlin-backed president in February.

Fighting rages almost every night, particularly around the rebel flashpoint of Slaviansk.

Dozens of people have been killed since Kiev launched what it called its "anti-terrorist operation" in mid-April.

In the east, the report said there has been a "worrying" rise in abductions and unlawful detention of journalists, activists, local politicians, representatives of international organisations and members of the military.

It highlighted its concerns about the deteriorating climate for the media operating in the east.

Rebels there have proclaimed independence in two regions following weekend referendums branded illegal by Kiev and the West.

In Crimea, the report said the annexation of the Black Sea peninsula by Russia in March, following a similar independence vote, was creating difficulties for many residents, particularly the ethnic Tatar community.

It listed cases of physical harassment and intimidation, restrictions on media and fears of religious persecution among practising Muslims in Crimea.

Russia has accused the authors of the report of carrying out a "political order to whitewash" the interim government in Kiev.

It also criticised what it said was a "lack of objectivity".