Russia attacked the Kyiv region with six missiles launched from the Black Sea, hitting a military unit in the village of Liutizh on the outskirts of the capital, Ukrainian officials said.
Meanwhile, five people were killed and 25 wounded in a Russian missile strike on a flight school in the central Ukrainian city of Kropyvnytskyi in the Kirovohrad region.
The latest attacks come as western military intelligence warned that Russian occupied forces were increasingly isolated in the Kherson region as the city's Antonivskiy Bridge, which was attacked by Ukrainian rockets earlier this week, was now “completely unusable”.
The UK Ministry of Defence said that Kherson was now “virtually cut off" from the other occupied territories and said Ukraine was “gathering momentum” in regaining the region.
President Volodymyr Zelensky vowed to “disrupt” Russia’s plans.
"We are doing everything to ensure that the occupiers do not have any logistical opportunities on our land," he said. "Whatever plans they have, we will disrupt them.
“And we will liberate our territory with military, diplomatic and all other available means until we reach the legal borders of Ukraine.”
However, Kirill Stremousov, a deputy head of the local administration in Kherson, said in an interview that the Ukrainian attack on the bridge "will not affect the course of hostilities in the region".
"We don't have a problem,” he added. "But every day a lot of Ukrainian rockets have been falling in the Kherson region and on the Antonivskiy Bridge. This is not an occupation - our future is with Russia."
Fifteen people were wounded in the Russian strikes on Kyiv, five of them civilians, Kyiv regional Governor Oleksiy Kuleba said.
Mr Kuleba linked the assaults to the Day of Statehood, a commemoration which Ukraine marked for the first time on Thursday.
"Russia, with the help of missiles, is mounting revenge for the widespread popular resistance, which the Ukrainians were able to organise precisely because of their statehood," Mr Kuleba said.