Explosions were heard in Kiev and other Ukrainian cities, a day after Russia accused Ukraine of carrying out a drone attack on the Kremlin.
Attacks were also reported in Zaporizhia and Odessa in the south.
The air strikes come as Ukrainian President Volodymyr Zelensky is scheduled to deliver a speech in The Hague as part of an unexpected visit to the Netherlands.
He will also visit the International Criminal Court, which is investigating alleged Russian war crimes in Ukraine.
Russia accused Ukraine of attempting to assassinate President Vladimir Putin, but Zelensky denied that his country had carried out the attack.
“We are not attacking Putin or Moscow. We are fighting on our lands. We are defending our villages and cities,” he said on Wednesday.
Zelensky was speaking in Finland, making a surprise visit and meeting his Finnish counterpart Sauli Niinistö and the leaders of Sweden, Norway, Denmark and Iceland.
During his visit to the Netherlands, Mr. Zelensky is expected to meet Dutch Prime Minister Mark Rutte. Dutch media said the two were likely to discuss Mr Zelensky’s demands for more military support – namely long-range weapons and fighter jets.
Back in January, Mr. Rutte said supplying fighter jets was not taboo, though such a move would be a “really big next step.”
In the wake of the alleged drone attacks, Russia has threatened retaliation whenever and wherever it deems it necessary.
On Wednesday, Russian strikes in the Kherson region of southern Ukraine killed 21 people. Officials said the victims included supermarket customers and energy company employees who were doing repairs.
And in the early hours of Thursday morning, sirens wailed across many Ukrainian regions. There were reports of powerful explosions in Kiev and Odessa.
At the same time, a drone has struck an oil refinery in southern Russia, setting part of it on fire — the latest in a series of explosions, fires and drone attacks that have occurred in Russia in recent weeks.
Some commentators have argued that the alleged drone strike on the Kremlin was carried out by Russia on purpose.
The Institute for the Study of War said it was “extremely unlikely that two drones could have penetrated multiple layers of air defense and exploded or been shot down over the heart of the Kremlin in such a way as to provide stunning images well captured on camera.”
It said that “Russia likely launched this attack in an effort to bring the war home to the Russian domestic public and create the conditions for a broader societal mobilization.”
Yuriy Ihnat, a spokesman for the Ukrainian Air Force, said he believed Russia launched the attack on the Kremlin in an attempt to “show some kind of escalation on the part of Ukraine”.
But other commentators have disputed this, saying that Russia would have little interest in making itself look “weak” by launching an offensive that makes the Kremlin look weak.
It would also raise questions about the extent of Mr. Putin’s protection — and about the effectiveness of Russia’s air defenses.
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