The former Soviet republic is fighting for its very survival after Russia seized Crimea and separatists launched an armed uprising in the eastern industrial belt, the worst crisis since independence over two decades ago.
"The first thing we must do is bring peace to all the citizens of Ukraine," said billionaire tycoon Petro Poroshenko, the clear favourite in a packed field of candidates to lead the former Soviet republic.
"Armed people must leave the streets of towns and cities," he said after casting his ballot in Kiev.
Turnout across the country was reported at over 38 per cent after seven hours of voting.
The West is closely watching the vote -- and Russia's actions -- fearing civil war could break out on Europe's doorstep.
Poroshenko called for "direct dialogue" with the people in Donetsk and Lugansk, where insurgents declared independence two weeks ago after referendums branded as shams by Kiev.
The ballot was called after Kremlin-allied president Viktor Yanukovych was ousted in February in the bloody climax of months of protests sparked by his rejection of a historic EU alliance.
But his fall set off a chain of tumultuous events which saw the Kremlin annex the Black Sea peninsula of Crimea and then pro-Russian rebels take up arms in the eastern hub of Ukraine's coal and steel industries.
In the separatist areas, voting was patchy with only 11 of the 34 electoral constituencies open, according to the central election commission.
"Ukraine is now another country so I don't see why we should take part in this election," said one woman in Donetsk called Elisabeta.
Election officials had reported numerous cases of intimidation and attacks and rebels threatened Saturday they would disrupt the vote "by force if necessary".
Russian President Vladimir Putin, facing the threat of further Western sanctions if Moscow interfered in the vote, appeared to make a major concession on Friday by saying he was ready to work with the new Kiev team.