"We expect the elections will go ahead as agreed, and we will of course recognise the results," Lavrov told Izvestia daily ahead of Sunday polls staged by two pro-Russian separatist regions to elect leaders and parliaments.
"We are counting on it being a free vote and that it will go ahead unhindered," Lavrov said of the simultaneous polls in the self-proclaimed people's republics of Donetsk and Lugansk.
Lavrov said the elections, opposed by Kiev, would be "important from the point of view of legitimizing the authority" of the regions' rebel leadership.
The Russian minister also said Russia was likely to recognize parliamentary elections held by Ukraine on Sunday, although it would wait for the verdict of the OSCE observers.
The Ukraine elections were not held in the rebel-held regions, home to three million voters.
"I think Russia recognises the results of the vote," Lavrov said.
"It's very important for us that authorities finally appear in Ukraine who are not engrossed in infighting or pulling the country now to the West, now to the East, but in the real problems that the government faces, as it thinks how to unify the country."
Lavrov said of the continuing violence in east Ukraine that "there were violations on both sides," largely due to the fact that the two sides cannot agree a demarcation line from which they should withdraw heavy armaments under the Minsk peace accord struck last month between Kiev, Moscow and the separatists.
"The line itself is still not finally agreed," Lavrov said.
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