Gladkov, writing on Telegram, also said that air defence units in his region had downed eight airborne objects late in the evening. There were no injuries but falling debris damaged roofs on industrial sites and homes.
In his account of the shelling deaths, Gladkov said that the victims - a couple, a grandmother and a boy of 17 - were killed when their house took a direct hit. He said a girl survived and was in intensive care.
Attacks on Belgorod have taken place frequently since 2022, but escalated in recent months, with 25 people killed in a single incident in late December. Thousands of Ukrainian civilians have been killed in Russian attacks.
Both sides say they do not target civilians.
(Reporting by Reuters; Editing by Mark Trevelyan, Ron Popeski and Sharon Singleton)
