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There are reports of a large number of explosions in the Ukrainian capital, Kyiv, and air raid sirens have been sounding.
In video on social media, air defence systems can be seen shooting down suspected Russian missiles.
Government messages warned people to keep away from windows as debris from intercepted missiles fell from the sky.
City mayor Vitali Klitschko said some rocket debris had fallen in central districts, including on the city's zoo.
There are reports of injuries.
In the past few days, President Volodymyr Zelensky has been on a European tour, in which he has been promised several billion dollars' worth of military equipment by Western allies, including UK Prime Minister Rishi Sunak and President Emmanuel Macron of France.
Since Russia invaded Ukraine on 24 February of last year, thousands of civilians and combatants have been killed or injured, cities and towns have been destroyed in fighting, and nearly 8.2 million Ukrainians have been registered as refugees in Europe, with 2.8 million of them in Russia.