Pro-Russian separatists have claimed a decisive victory in a self-rule vote they held in two eastern Ukrainian regions amid reports of at least one person being killed by Ukrainian security forces.
Pro-Russian separatist leaders said more than 70 percent of the electorate in the Donetsk and Luhansk regions -- home to 6.5 million of Ukraine's total population of 46 million -- voted in the referendum.
Roman Lyahin, the self-styled chief of the election commission of the "Donetsk People's Republic," said 89 percent had voted in favor.
However, there was no way to verify that claim, as no independent observers were monitoring the vote.
"These results only mean that the people of Donbas demand their opinion be respected, the norms of international law be respected. We demand the right to self-determination and we will strive toward this," Lyahin later told a press conference.
The preliminary vote count was announced just two hours after the polls closed in an election carried out with paper ballots.
In Luhansk, the other region voting in a self-rule referendum, a separatist election official said 96 percent of those who voted in Luhansk supported independence.
Oleksandr Malykhyn, the self-styled deputy chairman of Luhansk's election commission, added that turnout was 81 percent in Luhansk, which has a population of about 2.25 million people.
"Figures from fake referendums in eastern Ukraine likely to be fake. No way of even knowing official turnout," Swedish Foreign Minister Carl Bildt wrote on his Twitter account on May 11.
Earlier, Ukraine's Foreign Ministry called the referendums a "criminal farce" that was organized by Moscow. The Foreign Ministry said in a statement the vote was "inspired, organized, and financed by the Kremlin."
Serhiy Pashynskyy, the acting head of Ukraine's presidential administration, said no referendum was held by the separatists in "two-thirds of [the territory] of the Donetsk and Luhansk regions."
But the self-declared officials in the two eastern Ukrainian regions holding the referendums on self-rule claimed many voters took part in the polls.
Lyahin said, "What is happening in the Donetsk and Luhansk regions cannot be called a referendum," adding, "this is no more than an information campaign to cover up one's crimes."
Pavel Gubarev, the self-declared "people's governor" of Donetsk, told Russian television the vote was only the first step in building the country of "New Russia" in southeast Ukraine.
Long lines of voters were seen at several polling places in the city of Donetsk. But other areas in the region had no polling stations, and separatist officials said police prevented voters from entering other stations in western parts of the Donetsk region.
Oleksei Chmilenko, a self-declared leader of the Luhansk region, claimed turnout in that province was "over 80 percent."
Ukrainian acting President Oleksandr Turchynov warned that the vote was a "step into the abyss." Turchynov said the government was willing to negotiate with representatives from the east, but not with anyone he called "terrorists whose task is the destruction of the country."
WATCH: Donetsk referendum voters say they're "sick and tired" of Kyiv rule:
There were also reports of children voting, of people voting more than once, and of people claiming to vote for their spouses or other family members.
Voting was taking place in Slovyansk, with the self-styled separatist mayor of the city, Vyacheslav Ponomaryov, saying turnout would be "100 percent."
In Mariupol, the scene of deadly clashes in the last week, officials said only eight polling places had been set up for a city with a population of some 500,000 people.
This led to long lines outside the voting places, in one case with extra boxes being placed outside the building.
Shooting In Krasnoarmiysk
Tensions remained high in eastern Ukraine amid an ongoing military operation ordered by Kyiv against the rebels.
Ukrainian national guardsmen reportedly opened fire on a crowd outside a town hall in Krasnoarmiysk, 30 kilometers from Donetsk, and an official for the region's insurgents says there was at least one fatality.
The May 11 bloodshed in Krasnoarmiysk occurred hours after dozens of guardsmen came to the town and shut down voting in the referendum.
Separatist leader Denis Pushilin was quoted by the ITAR-TASS news agency as saying one civilian was killed, while videos posted on the Internet showed masked uniformed men shooting at the feet of unarmed protesters outside the Krasnoarmiysk town hall.
WATCH: In Luhansk, one voter says he doesn't want to see the region break away from Ukraine "yet," but hopes for the "federalization" of the country.
Early on May 11, an isolated clash occurred on the outskirts of the flashpoint town of Slovyansk as militants tried to recapture a TV tower, but polling in the center was unaffected.
Maja Kocijancic, a spokeswoman for EU foreign-policy chief Catherine Ashton, said on May 11 the EU will not recognize the results of "so-called" votes organized by separatists in eastern Ukraine.
The U.S. State Department said the referendums were illegal and "an attempt to create further division and disorder."
They were "null and void," French President Francois Hollande said on a visit to Azerbaijan.
Britain's Foreign Office issued a statement calling the "illegitimate, so-called referendum" regrettable.
It said that a nationwide presidential election Ukraine is scheduled on May 25 that will give "all Ukrainians... a democratic choice".
Britain also added its weight to a French and German warning of "consequences" against Russia if that election were to be scuppered.
A poll released on May 8 by the Pew Research Center in the United States suggested 70 percent of Ukrainians in the east want to stay in a united country, while only 18 percent back secession.
On May 12, EU Council President Herman Van Rompuy, who represents the bloc's 28 leaders, will fly to Ukraine to meet the interim government and discuss ways to stabilize the country ahead of the May 25 presidential poll.
With reporting by dpa, ITAR-TASS, Interfax, and AP