KYIV — Ukrainian shelling of the Russian city of Belgorod, close to the border with Ukraine, killed two people, Russian officials said Saturday.

A man and a woman died in the attack and three other people were wounded, the regional governor, Vyacheslav Gladkov, said on Telegram. It was the latest in exchanges of long-range missile and rocket fire in Russia’s war on Ukraine.

Five people were also wounded when a Ukrainian drone hit a car in the village of Glotovo, a little over a mile from the Ukrainian border, Mr. Gladkov said.

Also on Saturday, a Ukrainian drone attack caused a fire at an oil refinery belonging to Russian oil giant Rosneft in the Samara region, its regional governor, Dmitry Azarov, said. He said an attack on another refinery was thwarted. No casualties were reported.

The attacks come a day after a Russian assault on the Ukrainian port city of Odessa killed at least 21 people. The ballistic missile attack blasted homes in the southern city Friday, followed by a second missile that targeted first responders who arrived at the scene, officials said.

More than 50 people are still in the hospital following the attacks, Odessa’s deputy mayor, Svitlana Bedreha, said Saturday, according to Ukrainian state media.

President Zelensky had promised a “just response” to the attack in a video address Friday evening.

Saturday’s attacks occurred as Russians entered the second day of voting in an election that is all but certain to extend President Putin’s rule by another six years after he crushed dissent.