Pro-Russian activists in Ukraine's eastern Donetsk region have claimed a resounding victory in a "self-rule" referendum and said 89% voted in favor, according to BBC News.

In Luhansk, another eastern region, the results - also expected to show a strong backing - will be released soon.

Ukraine called the vote a "criminal farce" organized by Russia. The EU and U.S. also said the polls were illegal.

Pro-Russian forces claimed two people were killed by armed men loyal to Kyiv in the city of Krasnoarmiisk. But otherwise the voting passed off peacefully, the BBC says.

A number of towns in the two regions refused to hold the poll.

The referendums were held despite an earlier call by Russian President Vladimir Putin to delay them in order to create the conditions necessary for dialogue. The Kremlin has so far made no official comments after the voting ended.

The head of the self-proclaimed Donetsk People's Republic election commission, Roman Lyagin, told journalists several hours after the vote ended that 89.07% voted in favor of self-rule, with 10.19% against, with 0.74% of the ballots declared invalid.

Turnout was put at nearly 75%.

The Ukrainian Foreign Ministry condemned the polls, saying they were "inspired, organized and funded by the Kremlin".

In a statement, it said: "The Ukrainian people does not recognize any terrorist referendums in the Donetsk and Luhansk regions, and also in Crimea," in a reference to Russia's annexation of the southern peninsula in March.

A second round of voting is planned in a week's time, asking whether people support joining Russia. Organisers also say they will boycott Ukraine's presidential elections on May 25.