Russia's election commission said it was postponing the local vote in seven municipalities in the Kursk region, where Ukrainian troops launched an offensive more than two weeks ago, AFP reported.
The commission said on Telegram that the vote will take place when there is a "full guarantee of voter security".
But regional governorship elections due to start next week will go ahead as planned in the rest of the district.
Early voting for the gubernatorial election is expected to begin on August 28, and voting will close on September 8.
Two and a half years since the start of Russia's campaign in Ukraine, Kyiv has regained the initiative, sending troops into the western Kursk region on August 6.
Ukraine claims to have captured dozens of towns and villages in the region. Russia said more than 120,000 civilians had been forced to flee the area. | BGNES