The deaths of a man and a woman were reported by Vyacheslav Gladkov, governor of the Belgorod region where cross-border attacks from Ukraine have become part of daily life.
Meanwhile, Dmitry Azarov, governor of the Samara region 850 km (530 miles) southeast of Moscow, near the border with Ukraine, said the Syzran refinery was on fire but an attack on a second facility had been thwarted.
The Ukraine war has cast a shadow over voting in a three-day presidential election that is all but certain to hand incumbent president Vladimir Putin six more years in the Kremlin to cement his hardline rule.
The authorities are hoping for a high turnout to demonstrate that the country is united behind Putin.
Polls opened this week but voting has been marred by an uptick in fatal Ukrainian bombardments and a series of incursions into Russian territory by pro-Ukrainian sabotage groups.
Ukraine has staged repeated strikes this week on Russian refineries.
Putin, who cast his vote online, vowed a harsh response to the assaults and accused Kyiv of trying to "disrupt" his bid for another six-year mandate.
Overall turnout was nearly 38% by the morning of day two. Some of the highest rates - approaching 70% - were reported in the Belgorod region where the missile strike occurred and in Russian-controlled regions of Ukraine where Kyiv says voting is illegal and void.
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Source: PAP, Reuters, AFP