KYIV, Ukraine - A wave of Russian missiles hit Kyiv and other Ukrainian cities on Tuesday, killing 18 people and wounding more than a hundred, as Ukrainian President Volodymyr Zelensky vowed a forceful response.

Rescue workers in Kharkiv -- Ukraine's second-largest city, near Russia's border -- hauled survivors from smouldering piles of rubble as apartment blocks were set ablaze and toppled by the strikes, AFP journalists reported.

"Ordinary life is what Russia sees as a threat to itself. The state is a typical terrorist," a somber Zelensky said in his evening address to the nation, adding that 130 people had been injured in the attacks.

"Let them know in Russia that the Ukrainian character knows how to be far-reaching enough in response," Zelensky said. "The Russian war will inevitably be brought back home, back to where this evil came from, where it must be quelled."

Kharkiv regional governor Oleg Sinegubov said eight people had been killed in the overnight barrage that also wounded more than 50 people. Late in the evening Tuesday, Sinegubov reported a fresh round of strikes on Kharkiv that left four people injured.

Oleksandra Terekhovich ran into the corridor of her home for protection when she heard the first explosion. The second blast hit the building next door, shattering her windows and door, she said.

"There are no more tears. Our country has been going through what has been happening for two years now. We live with horror inside of us," she told AFP.

Interior Minister Igor Klymenko praised rescuers that he said pulled 27 survivors from rubble. He posted dramatic footage of workers cutting free a man who had been trapped in freezing temperatures for hours.

Russian forces had aimed to wrest control of Kharkiv -- the city worst hit in the overnight strikes -- early in their invasion, launched in February 2022.

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

- 'Really scary' -

In his address, Zelensky said Russia had launched nearly 40 missiles in the overnight barrage seeking to pierce Ukraine's air defence systems. While "a significant part" of them were downed by Ukrainian forces, other missiles hit 200 structures, including 139 residential buildings.

AFP reporters in Kyiv heard air raid sirens echo over the capital at night, followed by a series of loud blasts as defence systems targeted the aerial onslaught.

Mayor Vitali Klitschko said 20 people were wounded in the attack on Kyiv that set buildings and cars ablaze in central districts.

Daryna Bodenchuk, a 17-year-old interior design student, said she was in her Kyiv dormitory at the time of the strikes. They shook the building and blew open the door of the basement where she and others had taken shelter, she said.

"It's really scary. A window was broken also in our dormitory. It was loud," she told AFP.

In the region around Kyiv, officials said four people were wounded after residential blocks, private homes and farm buildings were damaged.

Further south, in the city of Pavlograd, the Dnipropetrovsk regional governor said one person had been killed and another wounded.

Separately, the governor of the southern region of Kherson, which the Kremlin claims is part of Russia, said a 70-year-old man had been killed by Russian forces, without giving details.

The US ambassador to Ukraine, Bridget Brink, said the attacks showed that Washington should double down on support.

"Ukraine needs our continued support now, to protect itself against these cruel attacks on civilians," she said on social media.

France's foreign ministry condemned Moscow's attacks on Ukrainian civilian infrastructure, saying "Russia is guilty of war crimes and bears sole responsibility for the escalation."

- Kremlin denies targeting civilians -

The Kremlin -- responding to questions from reporters about the attacks -- denied Russian forces had targeted civilian infrastructure and vowed to continue Moscow's nearly two-year invasion.

"Our military does not hit civilian facilities or residential neighbourhoods, and does not hit civilians -- unlike the Kyiv regime," spokesman Dmitry Peskov told reporters.

This was an apparent reference to an increase in fatal drone and missile attacks that Russian forces have blamed on Kyiv, targeting cities and energy facilities near the border.

And the Moscow-installed authorities in the Russian-occupied eastern Donetsk region said Ukrainian strikes have killed three people.