Loud explosions have been heard in parts of south-west Russia and occupied Crimea overnight.
Russian officials say the border city of Belgorod, where 25 people were killed on Saturday, came under attack again as well as Sevastopol in Crimea, where a Ukrainian missile was downed.
In recent days the aerial war between Russia and Ukraine has intensified.
Ukrainian President Volodymyr Zelensky says Russia used some 300 missiles and 200 drones over five days.
Russia launched its biggest aerial bombardment of the invasion late last week, killing more than 40 people.
Ukrainian forces responded with the attack on Belgorod in which more than 100 people were also injured.
More blasts were reported in Belgorod overnight into Wednesday, with the governor of the region saying several drones had been destroyed.
In Sevastopol – the biggest city in Russian-occupied Crimea – a missile was shot down over the port, the Moscow-installed governor, Mikhail Razvozhayev, said on Telegram. No casualties or damage were reported.
On Tuesday, Russian missiles hit Ukraine’s biggest cities including Kharkiv and Kyiv, killing at least five people and injuring dozens, local officials said.
One person was also reported killed in a Ukrainian attack on Belgorod.
Those attacks came after Russian President Vladimir Putin vowed to step up strikes in response to recent attacks by Ukraine.
In his nightly address on Tuesday, Mr Zelensky said Russia had fired “almost one hundred missiles of various types” that day.
They had, he said, been “specifically calculated by the enemy to cause as much damage as possible”.
Speaking to the BBC later, the Ukrainian ambassador to the US, Oksana Markarova, said Russia’s recent bombardment was “not something that came as a surprise” – but that for Ukraine to win the war they needed more weapons to respond and “just clearly send a message to Russia that they should stop”.
