Late-night Russian strikes on Kharkiv in eastern Ukraine left nine injured, the regional governor said Wednesday, just after a Russian missile barrage across the country that claimed more than a dozen lives.

The new Russian bombardments struck Kharkiv late Tuesday, hours after Moscow's missile attack killed at least 18 and wounded around 130 people.

The regional governor Oleg Sinegubov said Russian forces had fired S-300 surface-to-air missiles at the city, which lies next to Ukraine's border with Russia.

"As a result of the impact, nine people were injured, including one child, a four-year-old girl, who was given help at the scene," he said.

"Four people were hospitalised -- two men and two women," he added, noting that residential buildings, municipal offices and a educational facility were damaged.

Russian forces had aimed to wrest control of Kharkiv, Ukraine's second-largest city, early in their invasion, launched in February 2022.

Ukrainian forces pushed back Moscow's army, which has been routinely shelling the city since.

Separately, the governor of the southern Kherson region said Russian forces had killed a total of four residents of his region over the course of the day before.

Six more people were injured across the region, which the Kremlin claims is part of Russia, the governor, Oleksandr Prokudin, said on social media.

Both Russian and Ukraine have stepped up strikes on each other's cities and critical infrastructure. Kyiv has urged its allies to help bolster its air defence systems to ward off Russian attacks.