Rallies have been held in the eastern Ukrainian city of Donetsk in protest at pro-Russian separatism, at the instigation of Ukraine's richest man.
Steel magnate Rinat Akhmetov said "people are tired of living in fear and terror" and accused separatists of leading Ukraine towards "genocide".
Hundreds of people attended a rally in Mr Akhmetov's football stadium, while others blared car horns.
Separatist leaders have threatened to "nationalise" Mr Akhmetov's assets.
Meanwhile, Russia has said its troops on Ukraine's border are set to withdraw.
On Monday, Russian President Vladimir Putin said troops had been ordered to pull back - but Nato later said there was no sign of any redeployment.
On Tuesday, Russian Deputy Defence Minister Anatoly Antonov told the BBC the process of withdrawal "had been started already".
Moscow has had tens of thousands of soldiers on the border, raising fears of a takeover of eastern Ukraine following Russia's annexation of Crimea.
The BBC's Mark Lowen in Donetsk said Ukrainians who oppose the separatist gunmen made their voices heard on Tuesday.At the scene, Mark Lowen, BBC News, Donetsk
It was a noisy new strategy by those fighting for a united Ukraine. Cars swept through Donetsk, horns blaring, some waving the yellow and blue Ukrainian flag.
It had been planned as a march through the city of Mariupol on Monday but was cancelled at the last minute because of threats from the pro-Russia armed groups.
And so Rinat Akhmetov, whose company Metinvest is based in Donetsk, has now called for a car protest every day at noon. There are reports that some vehicles were attacked by the separatists as they drove past. But that didn't silence them.
This is the other side of eastern Ukraine to the one we've seen in the past few weeks: those angry at the separatism, at the attempted secession and at the masked gunmen roaming the streets. They want to vote in Sunday's presidential election and are determined to have their voices - and their car horns - heard.
Mr Akhmetov, whose fortune is estimated at more than $11bn (£6.5bn), is one of the most influential people in eastern Ukraine.
His enterprises are based in the Donbass - the industrial east of Ukraine - where the insurgency is at its peak and he is said to employ as many as 300,000 people.
His allegiances, however, have been in doubt because of past links with ousted pro-Moscow President Viktor Yanukovych and business links with Russia.
But in an address broadcast by his own Ukrayina TV channel, he issued a stinging criticism of the separatist rebellion.
He said Ukrainians - including his own employees - should stage a "peaceful warning protest" at their workplaces from noon on Tuesday, and that action should continue daily "until peace is established".
Otherwise he said he foresaw the "genocide of Donbass".
In response, Denis Pushilin, who heads the self-declared Donetsk People's Republic, said local industry would be "nationalised" if tycoons there refused to pay taxes to the rebel authorities.
"Akhmetov has made his choice. Unfortunately, he chose against the people of Donbass. Paying taxes to Kiev means financing terrorism in Donbass," Mr Pushilin was quoted as saying on the Donetsk People's Republic's Twitter feed.
Pro-Russian rebels have taken control of parts of eastern Ukraine including the major cities of Donetsk and Luhansk.
Ukraine is due to hold a presidential election on Sunday but the election may not take place in rebel-held parts of the east.
The UN refugee agency says at least 10,000 people have been displaced from their homes since the start of the crisis in Ukraine - most of them ethnic Tatars who have left Crimea, but also other ethnicities and those from mixed families.
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