Turnout was strong in the capital, Kiev, and the west but most polling stations remained closed across swaths of the rebel-controlled industrial east.
"Ukraine is now another country so I don't see why we should take part in this election," said one woman in the rebel-held city of Donetsk who gave her name as Elisabeta.
"It doesn't matter what the result is, it doesn't concern us today."
The west regards the vote as a crucial step in preventing Ukraine from disintegrating further after Russia seized the Black Sea peninsula of Crimea in March in retaliation for the ousting of pro-Kremlin president Viktor Yanukovych.
Ukraine's prime minister, Arseniy Yatsenyuk, had issued an appeal for voters to turn out in force on Sunday to "defend Ukraine" in the face of a crisis that has plunged east-west relations into a post-cold war low.
"I hope this election will finally bring peace to Ukraine," said 38-year-old businessman Oleh as he voted in the western nationalist bastion of Lviv near the Polish border.
But in the Donetsk region alone, where rebels declared independence earlier this month in defiance of Kiev, only 426 out of 2,430 polling stations were open, and none in the main city.
Even before polling day, election officials had reported numerous cases of intimidation and attacks on polling centres and rebels threatened on Saturday they would disrupt the vote "by force if necessary".
Violence had flared on the eve of the vote in eastern flashpoint of Slavyansk, where two western photographers and their Russian translator were wounded after being caught in gunfire between separatist and Ukrainian forces.
The Russian president, Vladimir Putin – authorised by parliament to invade Ukraine if necessary to "protect" ethnic Russians – had appeared to make a major concession on Friday by saying he was ready to work with the new Kiev leadership.
"We understand that the people of Ukraine want their country to emerge from this crisis. We will treat their choice with respect," he said.
Russia, threatened with further western sanctions if it disrupted the vote, also said it had started withdrawing from Ukraine's border about 40,000 soldiers and dozens of tank battalions whose presence had raised deep suspicions about the Kremlin's next move.
Ukraine has mobilised more than 82,000 police and 17,500 volunteers to ensure security for the vote, being overseen by 1,200 international monitors.
The packed field of candidates features clear frontrunner Petro Poroshenko – a billionaire chocolate baron and political veteran who sees Ukraine's future anchored to Europe – and 17 far less popular hopefuls that include ex-premier Yulia Tymoshenko.
The election should give the new president a stamp of legitimacy as he or she battles against the insurgency and tries to repair relations with Ukraine's former masters in Russia.
However, opinion polls show Poroshenko falling just short of the 50% threshold needed to avoid a second round on 15 June as well as and three weeks of further political uncertainty.
The snap ballot was called by Kiev's interim leaders who took power after Yanukovych fled in the bloody climax of months of protests sparked by his rejection of a historic EU alliance.
The charred buildings and flower-heaped barricades still crisscrossing Kiev's Independence Square – also the cradle of the 2004 Orange Revolution that first shook Russia's historic hold on Ukraine – serve as poignant testimony to the more than 100 people killed during the winter.
The authorities acknowledge problems staging polling in the steel mill and coal mine-dotted regions of Donetsk and Lugansk, where rebel leaders declared independent republics after hastily arranged referendums on 11 May.
At least 150 people have been killed since the separatists took up arms against Kiev in early April, according to an AFP tally based on UN and Ukrainian government figures.
Ukraine is hoping that up to $27bn (£16bn) in global assistance it won after the old regime's fall may help avert threatened bankruptcy and revive growth in the recession hit country.
But the new leadership will also have to negotiate with Russia over vital supplies of gas, with Moscow threatening to halt shipments if Ukraine does not pay a bill by early June.
Before voting got under way, Ukraine's interior minister, Arsen Avakov, said on his website that the election computer system had been the victim of a cyber attack and that counting would have to be done manually – but a spokeswoman later said the website had itself been hacked and the report was not true.
Voting closes at 5pm GMT, with the first results expected from 9pm.
"I hope this election will launch a process of change for the better … but I don't expect a magic wand," said Inna, a voter in the eastern city of Kharkiv that remains under Kiev's control.
Source: The Guardian Today