Organizers of Sunday's independence referendum in the eastern Ukrainian region of Donesk say 89 percent of those casting ballots voted in favor of splitting with Ukraine.
Although official results are not expected until Wednesday, the separatists say 10 percent rejected independence and that turnout was at 75 percent.
But a VOA reporter in Donetsk describes the election as a "shambles," with no clear procedures on tallying the ballots.
There is no information yet on results from Luhansk, the other eastern region that held an independence referendum Sunday.
The central Ukrainian government in Kyiv called the voting a "criminal farce," and the United States and its European allies denounced it as illegal.
It is still unclear whether so-called independence would mean more autonomy within Ukraine, an attempt to create an independent state, or a move to join Russia.
Russian President Vladimir Putin had urged the separatists to postpone Sunday's voting. The United States says it is disappointed the Kremlin did not use more influence to persuade the separatists to put it off.
A similar referendum in Ukraine's Crimean peninsula in March led to Russia's annexation of the region and the current crisis throughout eastern Ukraine, where pro-Russian separatists are in control of a number of towns and cities.
There was at least one incident of violence with pro-Kyiv militiamen exchanging fire with a group of what appeared to be civilians outside a town hall in Krasnoarmiysk. A leader of pro-Russian insurgents in the region said there were fatalities. The shooting occurred hours after the militiamen shut down a referendum there.
Interim Ukrainian President Oleksandr Turchynov has warned secession supporters that independence for the regions would be "a step into the abyss." He has appealed to the rebels to join talks on greater autonomy in the east.
State Department spokeswoman Jen Psaki said late Saturday the United States will not recognize the results of the referedums in eastern Ukraine. She said the polls "violate international law and the territorial integrity of Ukraine."
Psaki said the United States is "disappointed" Russia did not use its influence in the region to postpone the voting, despite Russian President Vladimir Putin's suggestion last week to delay the vote and his claim that Russian forces were pulling back from the Ukrainian border.
Psaki said the United States does not have any indication the Russian military is moving away from the border. She said Russian state media continued to "strongly back" the referendums "with no mention of Putin's call for postponement."
She said the Russian leadership must know that if it continues to destabilize eastern Ukraine and disrupt presidential elections later this month, "we will move quickly to impose greater costs on Russia."
The European Union has joined Kyiv and the U.S. in saying that it, too, considers the votes in eastern Ukraine as "illegal" and won't recognize their results.
"The so-called referenda in ... parts of the Luhansk and Donetsk regions were illegal and we do not recognize the outcome. Those who organized the referenda have no democratic legitimacy," Maja Kocijancic, a spokeswoman for EU foreign policy chief Catherine Ashton, said in e-mailed comments to Reuters.
She said holding the referenda ran counter to the objectives of an agreement reached by Ukraine, Russia, the European Union and the United States last month that aimed to defuse the Ukraine crisis.
Ukraine's Crimea region was annexed by Russia in March after a similar vote.
A senior Russian politician said on Sunday he had brought to Moscow a petition by residents of Moldova's Russian-speaking, breakaway region of Transdniestria that backs union with Russia.
Dmitry Rogozin's comments will likely rattle Moldova, a former Soviet republic which, like neighboring Ukraine, is seeking closer ties with Europe but faces stiff resistance from Moscow.
Transdniestria, which says it broke from Moldova in 1990, has long sought to join Russia and the West fears the narrow sliver of land on the Dniestr river will be Moscow's next target following its annexation of Ukraine's Crimea region in March and its support for pro-Russian separatists in eastern Ukraine.
Moscow said it has the right to protect its compatriots and Russian-speakers abroad but denies Western accusations that it is fomenting unrest in eastern Ukraine as a possible pretext for an intervention.
Additional information was provided by Reuters.