In Dagestan, one election official said he was prevented from doing his job by a crowd of men who blocked the ballot box.
But Ella Pamfilova, head of the Central Electoral Commission, said no serious violations had been registered yet.
“We have analysed and monitored everything we could, everything that has arrived. Thank goodness, it’s all rather modest so far,” she told a commission meeting while speaking about violations.
She had earlier said that anyone involved in violations would be caught.
Sunday’s vote was also the first in Crimea since Russia seized the region from Ukraine. Mr Putin was scheduled to speak at a rally scheduled for the fourth anniversary of the annexation – the same day as the election.
The annexation was bitterly contested by Kiev and ratcheted up tensions between Russia and the West. Russians living in Ukraine were unable to take part in Sunday’s vote because access to Russian diplomatic missions was blocked by the Kiev government.