Yanukovich is seen as the front runner in the poll, after beating Tymoshenko by 10 per cent in first-round polls last month.
Thumping rock music from the Yanukovich rally could be heard at Tymoshenko's somber "prayer for Ukraine", which was held outside Kiev's 11th-century Saint Sophia's Cathedral and drew hundreds of her backers.
"I ask God to give us wisdom, and I ask him to forgive all the unjust and dishonest acts committed by the authorities, which I represent too," Tymoshenko said, as she shared a stage with Orthodox priests.
Viktor Yushchenko, the outgoing president, ordered security measures to be taken to prevent post-poll violence.
Yushchenko ordered security forces to "cut short any manifestation of terrorism" and to improve security at the building of the Central Elections Commission in Kiev, where votes will be counted.
Tensions mounted this week as Tymoshenko accused Yanukovich of plotting to rig the vote and warned that she would mobilise her supporters for mass street protests in the event of vote fraud.
Supporters of Yanukovich, whose popularity has been boosted by a wave of discontent with the government's handling of the global economic crisis, dismissed her threat.
"What Ukraine needs now is bread, not revolution," Anna German, a prominent ally of Yanukovich and member of parliament from his Regions Party, said in a statement posted on the party's website.
Yanukovich's camp has in turn accused Tymoshenko and her supporters of planning to steal the election.
Earlier on Friday Yanukovich met with Mikhail Zurabov, Russia's ambassador to Ukraine, and pledged to improve ties with Moscow that deteriorated after the pro-Western Orange Revolution.
"I think our first task is simple: to turn the page on the past five years, leave them in the past and to continue the good, old traditions," Yanukovich told the envoy, according to a statement on his party's website.
Tymoshenko has cast herself as a pro-European champion of democracy, but she also has friendly ties with Vladimir Putin, the Russian prime minister.