Regional governor Vyacheslav Gladkov said the situation "continues to remain tense" in Belgorod, where Russia says 25 civilians including five children were killed in Ukrainian attacks on Saturday.
There was no word of any casualties from the latest attacks. Gladkov said the extent of damage would be assessed throughout the day.
Ukraine's escalation of attacks on Belgorod over the New Year period has come as Russia launched some of its most intense strikes on Ukraine since the war began almost two years ago. Kyiv said on Tuesday that Russia had launched well over 300 attack drones and missiles of various kinds at cities across Ukraine since Friday.
Belgorod, like other Russian regions on the border with Ukraine, has seen frequent low-level attacks since the start of the war, but Saturday's was by far the deadliest. President Vladimir Putin said it would "not go unpunished".
One person was killed and seven more wounded in the region on Tuesday, Russian authorities said.
In Wednesday's attacks, Russia's defence ministry said Ukraine fired six Tochka-U ballistic missiles and six guided missiles launched from a Vilkha heavy multiple rocket launcher.
Gladkov said Ukraine also launched several drones on the region and the city of Belgorod, which is the administrative centre of the region.
Reuters could not independently verify the reports. There was no immediate comment from Ukraine.
(Reporting by Lidia Kelly in Melbourne; Editing by Mark Trevelyan and Andrew Heavens)
