Russia has launched a "massive" drone attack on the capital, Kyiv Mayor Vitali Klitschko has said, while a maternity ward in Odesa has also been targeted.

The Odesa drone attack hit medical facilities and homes, killing a 59-year-old man and injuring four, Governer Oleg Kiper said, according to Agence France-Presse.

In the capital, emergency services were called to four districts a couple of hours after midnight on Tuesday, Klitschko said on the Telegram messaging app.

The latest attacks come after Russia's biggest drone strike on Ukraine on Monday, which Moscow said were retaliatory measures for Ukraine's recent attacks inside Russia. The covert "Operation Spider Web" targeted Russian bomber planes.

After the operation struck air bases deep inside Russia, US President Donald Trump called Vladimir Putin, and said the Russian president had promised to respond "very strongly" to the attacks.