Attacks were also reported in Zaporozhye and Odesa, in the south, according to the BBC.
The airstrikes take place at a time when Ukrainian President Volodymyr Zelenskiy is to speak in The Hague, during an unexpected visit to the Netherlands.
He will also visit the International Criminal Court, which is investigating alleged war crimes committed by Russia in Ukraine.
Russia has accused Ukraine of trying to assassinate President Vladimir Putin, but Zelenskiy has denied that his country carried out the attack.
On Wednesday, he declared: “We are not attacking Putin or Moscow. We are fighting on our territory. We defend our villages and cities”.
Zelenski spoke in Finland, where he made a surprise visit and met with his Finnish counterpart Sauli Niinisto and the leaders of Sweden, Norway, Denmark and Iceland.
During his visit to the Netherlands, Zelensky is expected to meet with Dutch Prime Minister Mark Rutte. Dutch media said the two were likely to discuss Zelenski’s requests for more military support – namely long-range weapons and fighter jets.
In January last year, Rutte said that providing fighter jets was not taboo, although such action would be “a very big next step”.
Following the alleged drone attacks, Russia has threatened to retaliate when and where it deems necessary.
On Wednesday, Russian strikes on the Kherson region in southern Ukraine killed 21 people. Officials said the victims included customers of a supermarket and employees of an energy company carrying out repairs.
And in the early hours of Thursday morning, air raid sirens sounded in many Ukrainian regions. Strong explosions were reported in Kiev and Odessa.
At the same time, a drone struck an oil refinery in southern Russia, setting part of it on fire – the latest in a series of explosions, fires and drone attacks in Russia in recent weeks.
Some commentators have argued that the alleged drone attack on the Kremlin was internally directed and deliberately staged by Russia.
The Institute for the Study of War said it was “extremely unlikely that two drones could have penetrated multiple layers of air defenses and detonated or been shot down right over the heart of the Kremlin in a way that provided spectacular images beautifully captured by cameras”.
He stated that “Russia probably staged this attack in an attempt to bring the war home to a domestic Russian audience and create the conditions for a wider mobilization of society.”
Iurii Ihnat, a spokesman for the Ukrainian Air Force, said he believed Russia staged the attack on the Kremlin to try to “show some kind of escalation on the part of Ukraine.”
But other commentators disagreed, saying Russia would have little interest in appearing “weak” by staging an attack that makes the Kremlin appear vulnerable.
It would also lead to questions about how well Putin was protected and about the effectiveness of Russian air defenses.
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