Pro-Russian rebels waging an insurgency for weeks have warned that they will disrupt the vote in the areas under their control in country's eastern rustbelt, "by force if necessary".
Prime Minister Arseniy Yatsenyuk issued an appeal for the country's 36 million voters to turn out in force today to "defend Ukraine" in the most important election since independence in 1991.
"This will be the expression of the will of Ukrainians from the west, east, north and south," he said yesterday.
President Vladimir Putin -- still authorised by parliament to invade Ukraine if necessary to "protect" ethnic Russians -- appeared to make a big concession on Friday by saying he was ready to work with the new Kiev team.
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"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 also says it has started withdrawing from Ukraine's border around 40,000 soldiers and dozens of tank battalions that had been ready to advance at a moment's notice.
Before voting got under way Ukraine's Interior Minister Arsen Avakov said on his website said that the election computer system had been the victim of a cyber attack and that counting would have to be done manually -- but a spokesman later said that his website had itself been hacked and the report was not true.