The Ukrainian cities of Kherson and Kramatorsk were subjected to rocket fire and air strikes over the past 24 hours, BNR reported.
One local resident was killed and 11 were injured.
In the evening, Russia attacked the capital Kiev with ballistic missiles. Explosions are reported, but no damage or casualties.
Emergency power outages continue in much of Ukraine.
Nuclear power plants are operating at reduced capacity after yesterday's Russian bombing of their associated substations.
Odessa has been attacked with drones from the Black Sea, explosions echoed in the city, the head of the Odessa City Military Administration, Sergei Lisak, announced on his Telegram channel, quoted by BTA.
Nearly 20 drones are moving from the sea in all areas of the city, local channels in the application report.
The air alert was announced at 00:08. Regional authorities are urging residents to take shelter in bomb shelters.
As a result of the strike following the massive attack on the Ukrainian Black Sea city, a fire broke out in one of the blocks of a residential complex in the Primorsky district, local Telegram channels reported. The fire also engulfed cars.
There have been no reports of casualties so far.