Reuters reporters used mechanical counters to count everybody who cast a ballot at the 12 polling stations they monitored from open to close on Sunday.
In some places, the discrepancies between the official count and the Reuters tally were small, with local election officials putting it down to the margin of error. But in nine of the 12 polling stations, the discrepancies were 10% or greater.
The biggest divergence, as a share of the total vote, was in polling station number 265, inside a technical college in Simferopol, Crimea. Moscow annexed the region from Ukraine four years ago.
Reuters reporters saw 797 voters at that station, while the official figures state that 1,325 people voted on the day and in person.
Asked about the discrepancy, the chairwoman of the polling station's election commission, Oksana Mediyeva, said independent monitors had watched the vote and had raised no issues.
Kremlin spokesman Dmitry Peskov said there were established procedures for reporting election violations. "If these reports from the respected Reuters agency are backed up by corresponding statements to law enforcement agencies from the observers who were at each polling station, then it's a worry. If they are not backed up, then it does not worry us at all."