Pro-Russian separatists in Ukraine's eastern Donetsk region have claimed a resounding victory in a "self-rule" referendum, saying 89% voted in favour.
In Luhansk, another eastern region, the results - also expected to show a strong backing - will be released soon.
BBC reporters at polling stations spoke of chaotic scenes, no voting booths in places and no electoral register.
Ukraine called the vote a "criminal farce" organised by Russia. The EU and US also said the polls were illegal.
Separatists claimed two people were killed by armed men loyal to Kiev in the city of Krasnoarmiisk.
But otherwise the voting passed off peacefully, the BBC's Richard Galpin in Donetsk reports.
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 favour of self-rule, with 10.19% against, with 0.74% of the ballots declared invalid.
Results the Luhansk region are expected later on Monday.
Donetsk separatist leader Denis Pushilin told one Russian news agency that once the results were confirmed, all Ukrainian military troops in the region would be considered "occupying forces".
The Ukrainian foreign ministry condemned the polls, saying they were "inspired, organised and funded by the Kremlin".
In a statement, it said: "The Ukrainian people do not recognise 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 25 May.
NEW SANCTIONS WARNING
Ukraine's interim President Olexandr Turchynov has admitted many in the east supported pro-Russian militants, but warned the referendums were "a step towards the abyss".
The EU and US have also condemned the referendums, amid fears Ukraine could be sliding to civil war.
A Pew Research Centre survey suggested a majority even in eastern Ukraine - 70% - wanted to remain in a united country, despite concerns about governance.
Russia annexed Ukraine's southern autonomous republic of Crimea after a March referendum.
Russia is estimated to have some 40,000 troops near the border and says they have been pulled back, but Nato says it has seen no sign of this.
EU leaders have warned Russia it faces further sanctions if Ukraine's presidential election fails to go ahead. EU foreign ministers are due to meet in Brussels to discuss the issue.