Officials in Ukraine said Russia's overnight bombardment was the largest since the war began.
Ukraine's air force said that 805 drones and 13 missiles were fired, but air defenses managed to shoot down 747 drones and 4 missiles.
The air force said that there had been nine confirmed missile hits and 56 drone strikes in locations across Ukraine.
The building that was damaged in Kyiv, is home to Ukraine's Cabinet and is where various ministers have their offices.
"For the first time, the government building was damaged by an enemy attack, including the roof and upper floors," said Ukraine's Prime Minister Yulia Svyrydenko.
"We will restore the buildings, but lost lives cannot be returned," Svyrydenko said.
The attacks come amid efforts to bring Ukraine's President Volodymyr Zelenskyy and Russia's Vladimir Putin to negotiate an end to the war.
Zelenskyy has said he is ready to meet Putin, who invited the Ukrainian leader to Moscow for talks. Zelenskyy rejected the invite and said Putin could come to Kyiv.
Russia's overnight drone attacks kill at least two in Kyiv
A series of Russian strikes across Ukraine overnight left at least two people dead and several others injured, Ukrainian officials reported.
In Kyiv, falling debris from downed drones started fires on top of a 16-story residential building and two nine-story buildings, according to Mayor Vitali Klitschko.
Tymur Tkachenko, the head of Kyiv's city military administration, said that among the dead was a one-year-old child whose body was uncovered from the rubble by rescuers.
According to Reuters, witnesses heard a series of explosions shaking the Ukrainian capital city, which they believe were air defense units conducting operations.
Explosions were also reported in the cities of Odesa, Kharkiv, Dnipro, Zaporizhzhia, and Kryvyi Rih.
Poland, which is Ukraine's neighbor to the west, scrambled its fighter jets during Russia's air raid to protect its own air space.
Russia currently occupies about 20% of Ukraine’s territory. Meanwhile, diplomatic efforts to reach a ceasefire and achieve lasting peace have stalled.
