GENEVA — Amid fears of escalating violence in eastern Ukraine, the United Nations called on Tuesday for action to counter misinformation and hate speech used as propaganda and urged the authorities in Crimea to account for killings, torture and arbitrary arrests in the buildup to the March referendum that led to its annexation by Russia.

“Facts on the ground need to be established to help reduce the risk of radically different narratives being exploited for political ends,” the United Nations’ high commissioner for human rights, Navi Pillay, said in a statement released with a report on human rights in Ukraine and Crimea, which until last month was an autonomous region of Ukraine.

“People need a reliable point of view to counter what has been widespread misinformation and also speech that aims to incite hatred on national, religious or racial grounds,” she added.

The United Nations report came as Prime Minister Dmitri A. Medvedev of Russia, on a visit to Crimea, said in a post on Facebook that eastern Ukraine was “on the brink of civil war.”