Cities across eastern Ukraine have been overtaken by pro-Russian protesters in recent weeks, leading the Ukrainian military to respond with force in some areas.

Cities across eastern Ukraine have been overtaken by pro-Russian protesters in recent weeks, leading the Ukrainian military to respond with force in some areas.

Cities across eastern Ukraine have been overtaken by pro-Russian protesters in recent weeks, leading the Ukrainian military to respond with force in some areas.

Residents of two regions of eastern Ukraine turned out in significant numbers Sunday to vote in support of self-rule in a referendum that threatens to deepen divisions in a country already heading perilously toward civil war.

The wording of the referendum was vague, asking whether voters favored self-determination rather than outright independence or joining Russia. That meant some of those voting yes wanted more autonomy but not necessarily to split from Ukraine.

But the vote infuriated the Ukrainian government. The Foreign Ministry called it a “criminal farce” arranged by a “gang of Russian terrorists,” reflecting the government’s view that Russian agents are behind the breakaway movement. Many residents who oppose the separatist movement boycotted the vote.

Both the European Union and the Obama administration said they would not recognize the results of the balloting in the Donetsk and Luhansk regions, which they called illegal.

Late Sunday night, Roman Lyagin, head of the separatist election commission in Donetsk, said that nearly three-quarters of the 3.32 million eligible voters in the region had cast ballots, a figure that was not possible to confirm independently. Just over 89 percent of voters approved the measure, he said. Figures for Luhansk were not immediately available.

The vote will complicate Ukraine’s efforts to reestablish order in the wake of a revolt that ousted the country’s pro-Russian president in February and prompted a backlash in the east. Ukraine has scheduled national elections for May 25. But given Sunday’s result, Lyagin said, “it is not logical to have the presidential election here on the territory of the Donetsk People’s Republic.” The U.S. and European governments have threatened Russia with further sanctions if the national vote is disrupted.

Ukrainian troops have been trying to wrest back control of eastern cities where separatists have seized government buildings and set up checkpoints manned by militias. Despite the government’s condemnation of the vote, its armed forces generally allowed balloting to proceed Sunday. But Ukrainian national guardsmen shut down the voting in the eastern city of Krasnoarmeysk and later fired into a crowd outside the town hall, wire services reported. The Associated Press said one of its photographers saw two people lying motionless on the ground after the clash. Denis Pushilin, a leader of the rebellion, told the Itar-Tass news agency that there were an unspecified number of deaths.

Separatist leaders have in the past come out clearly in favor of independence or of union with Russia, and they have suggested that another referendum to decide that question could take place at a later date. Lyagin said there was no plan for a quick second referendum, but he did not deny that one might eventually occur.

Russia is almost certain to embrace the vote as legitimate. In a pre-recorded speech that blared over loudspeakers in a rebel military camp in Luhansk, Russian nationalist politician Vladimir Zhirinovsky congratulated people for their “absolute victory.”

“We’ll live a peaceful life in Russia together, and Kiev will always lose,” Zhirinovsky said. Russia has massed roughly 40,000 troops on its border with Ukraine and has threatened to intervene if the rights of ethnic Russians are violated.

Many observers say the referendum lacks any credibility. Names were checked against a 2012 voters’ list, but anyone who turned up with a passport was allowed to vote, even if they weren’t on the list. Indeed, in one polling station in the city of Mariupol, many people brought multiple passports on behalf of relatives and openly filled out two, three or even four ballot slips themselves.

The ballots lacked markings that could prevent them from being widely copied. The people staffing the polling stations and counting the ballots were activists who supported a yes vote. There were no international oversight missions.

Nonetheless, many people here — at least those who voted — will see it as a powerful expression of popular will.

At the very least, the lines of voters appeared to reflect a significant protest vote against the central government in Kiev.

But whether residents were seeking to join Russia was unclear. The ballots asked voters whether they supported what could be translated variously as “independence,” “sovereignty” or “self-determination” for the Donetsk and Luhansk regions.

“My problem is not Ukraine, it is the authorities in Kiev,” said Anton Karpov, a 31-year-old employee of a coal mine.

Polls have indicated that most residents of eastern Ukraine would prefer to stay part of that country. That’s a far different attitude than in Crimea, where residents voted in an impromptu referendum in March to leave Ukraine. The peninsula was then annexed by Russia, a move that was not recognized internationally.

Still, many residents of eastern Ukraine are deeply unhappy with the Western-leaning national government that came to power in February after President Viktor Yanukovych was forced from office; many consider the new government to be illegal and in league with ultra-nationalist groups. Some worry that the large population of Russian-speakers living in the east will be treated as second-class citizens by the new government. Their fears have been magnified by aggressive Russian propaganda.

Opponents of the separatist movement largely stayed away from polling stations Sunday. The referendum “is not legal,” said a 35-year-old businessman who gave his name only as Dmitry and was walking in a Donetsk park with his wife. He said he would not vote. “It’s just people with guns,” he said. “It is not a democratic referendum.”

There were no independent exit polls Sunday. But it did appear that turnout was relatively high. Journalists from several Western news organizations interviewed 186 residents in the Donetsk region, away from polling stations, and found that 116 had cast ballots or intended to. A total of 122 favored self-determination. The results were not scientific but reflected the level of interest in the referendum.

Residents’ attitudes appear to have hardened considerably with the deaths of dozens of pro-Russian activists in the city of Odessa this month and with reports that troops fired at a crowd in Mariupol last week.

“I am not against Ukraine. My children go to a Ukrainian school,” said Elena Voronkova, a 39-year-old businesswoman who voted yes. “But I want peace, stability and not to be afraid.”

Some residents said they wanted more autonomy for their region in a unified Ukraine. Others were openly in favor of joining Russia.

“My soul is asking, my motherland is asking” for a union with Russia, said Vyachesla, 73, a retired lawyer who did not want to give his last name. “I am voting no to fascism and no to the Kiev junta.”

Voting in Donetsk appeared orderly at many polling stations. People lined up to record their names and then stepped into curtained booths to mark their ballots before dropping them into containers decorated with the black, blue and red flag of the self-proclaimed Donetsk People’s Republic.

In Horlivka, a tiny suburb about 15 miles from the city of Donetsk, turnout was heavy.

Sergei Vasilyev, 28, who backs the separatist cause, said he was surprised by the size of the crowd, noting that it appeared to top any turnout he had seen in previous presidential elections. “I thought we would be much fewer,” Vasilyev said.

But those in Horlivka who support a united Ukraine said they had no plans to vote or felt intimidated about voicing their views. Some mentioned cultural and generational divides that have fueled separatist tensions and are likely to be reflected in the vote.

“Only old people are happy about it,” said Vika, a student in a technical college who was discussing the referendum with friends in a cafe and declined to give more than her first name. The elderly had grown up in a Ukraine that was part of the Soviet Union, which collapsed in 1991. “Young people go to vote because we are afraid of being killed in Horlivka,” she said.

The rebels rejected Russian President Vladimir Putin’s surprise call last week for the referendum to be postponed, arguing that they would lose popular trust if they did so.

Nemstova reported from Luhansk and Horlivka. Alex Ryabchyn in Donetsk and Fredrick Kunkle in Kiev contributed to this report.