A man looks at a bullet shell next to a destroyed car after a gunfight between pro-Russian militiamen and Ukrainian forces in Karlivka, Ukraine, on Friday, May 23. Tensions remain high across the country's east, where pro-Russian separatists staged referendums on independence earlier this month.
Crisis in Ukraine
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While saying he would respect the Ukrainians' choice, Putin reiterated Russia's assertion that according to Ukraine's Constitution, Yanukovych remains the legitimate president.
He also questioned whether the election should be held now given the current violence in eastern regions of the country.
Russian state media cited Deputy Foreign Minister Alexei Meshkov as saying Friday that Russia would decide whether or not to recognize the polls only after the vote takes place.
"Let's wait for the elections first. Naturally, when Russia considers this issue (on legitimacy) we will take into account all factors," official news agency ITAR-Tass quotes Meshkov as saying.
Unpaid gas bills
Addressing business leaders, Putin said Russia had tried to help Ukraine in its difficult economic situation.
But he said Ukraine must pay off the hefty arrears owed to Russian energy giant Gazprom for natural gas.
"The risks today of delivery of the gas supply are not our fault but quite honestly, everyone understands that this is because of the transit country Ukraine, which has abused its situation," he said.
"We provided Ukraine with 10 billion cubic meters of gas for free," he added. "This is not sensible; this is really stupid, and we must have limits."
Asked if he could work with a Ukrainian government led by Petro Poroshenko, a billionaire businessman and seasoned politician seen as a front-runner in Sunday's election, Putin joked that he could -- if Ukraine pays the $3.5 billion it owes.
Kiev and European Union leaders have urged Russia not to use the energy supply as a weapon.
Putin also called for dialogue between Russia and the United States over the crisis in Ukraine, suggesting Washington had not taken Russia's interests into account until now.
He was critical of the sanctions imposed on Russia by the West, warning that they would have a "boomerang" effect and hurt the United States and EU.
The Russian President also suggested the U.S. sanctions could be a ploy to give American companies a competitive advantage in Europe.
At the same time, Putin said he was "optimistic" the crisis in Ukraine could be resolved.
And he said Russia was continuing to cooperate with the United States in areas such as anti-piracy efforts and access to Afghanistan.
Putin also defended Moscow's recent disputed annexation of Crimea, saying its action had prevented violence there and ensured the "possibility of free will for the people" who chose to join Russia in a democratic referendum.
Separatists, right-wing militants clash
Clashes between separatists and pro-Ukrainian militants, the latter from the so-called "Donbass battalion" and far-right group Right Sector, were reported Friday morning near the town of Karlivka.
According to the Donetsk state administration, one person died and nine were wounded there.
The chief of staff for Right Sector, Andriy Denysenko, earlier told CNN that the pro-Ukrainian forces wanted to take down a separatist checkpoint in the area but were "attacked" by about 100 separatists.
After a battle lasting about two hours, he said, most of the pro-Ukrainian forces were able to pull back to a Ukrainian military checkpoint near Krasnoarmiysk, but four remained trapped in a cafe.
Pro-Ukrainian forces said they were either killed or taken hostage, Denysenko said. But he denied reports that 10 Right Sector members had been killed.
Disturbances were also reported Friday in Slovyansk, a stronghold for the separatists in the eastern Donetsk region.
A CNN team in Slovyansk heard about 10 explosions in what sounded like the outskirts of the town, following shelling overnight around a militant barricade.
The self-declared mayor of Slovyansk, Vyacheslav Ponomaryov, has said that anyone who tries to vote in the presidential election will be arrested.
Speaking with CNN, Ponomaryov also suggested that a gap had opened up between his group and fellow separatist leader Denis Pushilin in the regional capital, Donetsk.
Divisions within the separatist movement are likely to make future political negotiations more difficult.
In another indication of the heightened tensions, Ukraine's Border Service said Friday that its guards had thwarted another attempt by armed men illegally to bring weapons and ammunition over the border from Russia.
Journalist Victoria Butenko reported from Kiev, and CNN's Laura Smith-Spark reported and wrote from London. CNN's Nick Paton Walsh and Ben Brumfield contributed to this report.