Ukrainian forces in Kyiv said on Friday they shot down 36 Russian missiles and drones in and around the capital overnight, with two people injured by falling debris before authorities lifted air raid alerts across most of the country.

Russia has launched about 20 missile and drone attacks on Kyiv since the beginning of May, a surge in strikes that the government says appears aimed at derailing Ukraine's preparations for a major counter-offensive.

An Air Force statement said its air defenses had shot down 15 cruise missiles and 21 drones. It said a wave of drones had been launched late on Thursday, followed by a volley of cruise missiles as people slept at around 3 a.m. local time.

"The occupiers are not stopping their attempts to terrorize the Ukrainian capital with strike drones and missiles," it said.

The capital's military authorities, writing on Telegram, praised the city's air defenses and said there were no reports of damage or casualties.

Kyiv Mayor Vitali Klitschko, who earlier reported two separate waves of attacks, wrote on Telegram that there had been no calls for rescue services.

In the region outside Kyiv, authorities said two people were injured as a result of falling debris, including a child.

"In addition, the falling debris damaged five private houses," the state administration said on the Telegram messaging service.

Ukraine says it destroys the majority of the missiles and drones Russian forces use in attacks, but a nine-year-old girl was among three people killed in a missile strike on Kyiv on Thursday after the shelter they rushed to failed to open.

President Volodymyr Zelenskyy said if local officials were unable to provide protection, they could be prosecuted.

Russian officials reported more cross-border shelling from Ukraine on Friday and said two long-range drones had attacked fuel and energy infrastructure further north in Russia, but that no fires were reported there and there were no reports of injuries.