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Residents of the eastern Ukraine regions controlled by Russia-backed separatist rebels voted Sunday for local governments in elections denounced by Kiev and the West.

The elections were to choose heads of government and legislature members in the self-proclaimed Donetsk and Luhansk People's Republics, where separatists have fought Ukrainian forces since the spring of 2014 in a war that has killed more than 10,000 people.

Although a 2015 accord on ending the war calls for local elections in Donetsk and Luhansk, critics including Ukraine's president, the U.S. and the European Union say the vote is illegitimate because it is conducted where Ukraine has no control.

But the separatists say the vote is a key step toward establishing full-fledged democracy in the regions.

"It's another exam for the civic position, political position for the whole Donetsk Republic," said Denis Pushilin, who became acting head of the Donetsk separatist regime since predecessor Alexander Zakharchenko was killed in a restaurant bombing in August.

His Luhansk counterpart, Leonid Pasechnik, said Sunday that "we are a free republic, a free country" and denied that the voting was being held contrary to the 2015 agreement signed in Minsk.

Last week, the European Union condemned the elections as "illegal and illegitimate ... they are in breach of international law, undermine the commitments taken under the Minsk agreements and violate Ukraine's sovereignty and law."

"These are elections for entities that have no legitimacy under the Ukrainian constitution," Kurt Volker, the U.S. special envoy for Ukraine, said last week.

"The people in eastern Ukraine will be better off within a unified Ukraine at peace rather than in a second-rate police state run by crooks and thugs, all subsidized by Russian taxpayers," he said Sunday on Twitter.

Both regions reported voter turnout of more than 70 percent as of two hours before the polls closed at 8 p.m. (1700 GMT).

Andrei Yermolaev, an analyst at the New Ukraine think-tank in Kiev, said "conducting the elections despite the opinions of Kiev and the West means that the Kremlin completely controls the situation in the region and intends to use this 'frozen conflict' as a lever of pressure on the Ukrainian authorities."

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Jim Heintz in Moscow contributed to this story.