Voting is under way in Ukraine's presidential election, three months after the ouster of the country's pro-Russia leader.
The vote comes with pro-Russian separatists in control of much of two eastern regions.
The country's Central Election Commission said that by 3:00 p.m. Kyiv time, national turnout stood at more than 40 percent.
In the capital, Kyiv, long queues were reported at some polling stations, while most polling stations remained closed in the eastern regions of Donetsk and Luhansk, where separatist militants are trying to block the process.
The regional administration in Donetsk said that just 426 of 2,430 polling stations in the eastern region were open, and none in the city of Donetsk itself, where separatists publicly smashed ballot boxes.
In the neighboring region of Luhansk, the head of the Central Election Commission, Mikhail Okhendovsky, told reporters that only two of the 12 polling districts were open for voting.
The Central Election Commission said that voter turnout was around 17 percent in Luhansk and almost 11 percent in Donetsk by around 3:00 p.m. Kyiv time.
Luhansk and Donetsk declared independence after referendums on 11 May.
After casting his vote in Kyiv, acting Prime Minister Arseniy Yatsenyuk warned: “All attempts to wreck the election made by Russia and Russian-funded terrorists are bound to fail."
Kyiv accuses Moscow of backing the separatists.
Russian President Vladimir Putin has promised to respect the outcome of the vote and work with the new Ukrainian administration.
Russia annexed Ukraine's Crimea region in March after a disputed referendum there.
Eighteen candidates are competing to become Ukraine's next leader.
Polls show billionaire confectioner Petro Poroshenko with a commanding lead but short of the absolute majority needed to win in the first round.
(WATCH: In Central Ukraine, Voters Queue To Cast Ballots)
After casting his ballot in Kyiv, Poroshenko called for "direct dialogue" with the people of Donetsk and Lugansk regions.
His nearest challenger is Yulia Tymoshenko, the former prime minister and one of the leaders of the 2004 "Orange Revolution," who is far behind in the polls.
After voting in the central city of Dnipropetrovsk, Tymoshenko said, "It is time to hold a referendum on joining NATO to restore peace in Ukraine."
If no candidate wins over 50 percent of the vote, a runoff election will be held on June 15.
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Yatsenyuk, in a statement on May 24, told Ukrainians they have a responsibility to vote despite threats by "bandits sponsored from abroad" to disrupt the election.
Yatsenyuk said he was sure the winner of the election will make a priority of signing a key political and free trade agreement with the European Union.
The refusal of Moscow-backed President Viktor Yanukovych's to sign the deal triggered months of mass protests that ended when he fled to Russia in February.
Yatsenyuk said the vote will be an expression "of the will of Ukrainians from the west, east, north and south."
In eastern Donetsk and Luhansk regions, however, pro-Russian rebels have seized or blocked the offices of around half of the election commissions, in some cases kidnapping and intimidating election officials.
Denis Pushilin, one of the leaders of the self-styled "Donetsk People's Republic," threatened on May 24 that "if necessary" the insurgents will use force to prevent voting taking place.
Authorities say they have mobilized tens of thousands of police and volunteers to try to ensure security on polling day.
Over 1,000 OSCE observers were checking polling stations and counts across the country outside of Donetsk and Luhansk.
Polls close at 7:00 p.m. Central European Time.
Exit polls shortly thereafter should give a good indication of the result, although official preliminary results are not expected until May 26.
In Donetsk, hundreds of pro-Russian separatists, including some masked gunmen, gathered outside the walled home of industrialist Rinat Akhmetov, reportedly threatening to "nationalize" his property.
Akhmetov, a coal and steel billionaire, has urged people to vote and accused the separatists of actions that could lead to "genocide."
Akhmetov's suburban residence is protected by armed security guards.
Akhmetov, whose businesses employ about 300,000 people, has encouraged his workers to take part in peace rallies in the past few days against the separatists and in favor of Ukrainian unity.
Ousted Ukrainian President Viktor Yanukovych remains in exile in Russia, and has kept a low profile ahead of the voting.
Based on reporting by AP and Reuters