The strikes mostly targeted residential areas, injuring at least 12 civilians, and come as a limited ceasefire between the two sides was agreed on Tuesday.
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At least 12 people have been injured, including a 12-year-old girl, in a Russian strike late on Wednesday on the Ukrainian city of Kharkiv, according to local officials.
The State Emergency Service (SES) reported that Russia launched a "massive drone" attack, with explosions causing fires in various locations.
A video shared by them shows the moment of one of the explosions.
The attacks targeted both civilian infrastructure and a residential sector of the city and sparked at least four separate fires, causing damage to a number of buildings.
The largest of the fires covered an area of 2,500 square meters in what the SES described as a production facility.
A total of 117 emergency service personnel were involved in the rescue operation, they said.
Ukraine's President Volodymyr Zelenskyy said in a social media post that the cities of Sumy and Dnipro had also been attacked by Russia.
Russian drone strikes targeted the city of Okhtyrka, in the Sumy region, sparking a fire and causing damage to a number of buildings, Ukraine's State Emergency Service said on Wednesday morning.
Nobody was injured in the attacks, and rescuers were able to extinguish the fire that broke out, it said.
A number of civilians were evacuated from damaged buildings, which included residential structures, an administrative building and a number of shops.
The strikes occurred as ceasefire talks were underway between US and Russian officials in Saudi Arabia.
On Tuesday, both Ukraine and Russia said an agreement to stop using force in the Black Sea had been reached.
Meanwhile, Russia's Defence Ministry said one Ukrainian drone was shot down overnight over the Bryansk region, causing a power shortage.
"Against this background, it is definitely inappropriate and unhelpful to talk about easing pressure on Russia or lifting sanctions," Zelenskyy wrote on social media.
"Pressure on Russia is needed to save people's lives and for diplomacy to work faster and more fully," he added.