One of the dead had been in the parking lot of a maternity hospital, said Mayor Vitali Klitschko, writing on the Telegram messaging app. Three of the six injured were medical personnel and two of those hurt were in a serious condition.
Part of the hospital facade was damaged, as was a nearby clinic.
Debris hit the ground in three districts of the capital and Klitschko said part of a residence had also been destroyed.
"In the Dniprovskyi district, debris fell into the yard of a private property," Klitschko wrote. "People may be trapped under rubble". He urged residents to remain in shelters.
Kyiv's military administration said a 16-storey residential building was damaged, along with private homes.
Ukrainian President Volodymyr Zelenskiy decried the new Russian missile attack and said the strikes were recurring because of insufficient pressure on Moscow.
"Every such attack occurs because the pressure on the aggressor has not become total and Russia believes it can continue to rely on ballistic terror," Zelenskiy, attending the UN General Assembly in New York, wrote on social media.
He said the attack took place as he was discussing the newly approved Lindsey Graham Russia sanctions law with members of the US Congress.
"Right now, the United States has the opportunity to respond strongly. We need ballistic interceptors to protect lives. We need to implement sanctions against Russia and those who help it earn money," he added on the messaging app.
In the Black Sea port of Odesa, the head of the city's military administration, Serhiy Lysak, said on Telegram that overnight Russian strikes had damaged residences and medical and educational institutions. He gave no further details.
Earlier, Ukraine and Russia voiced an interest in a limited ceasefire involving grain and energy-related targets, US Secretary of State Marco Rubio said after meeting Russian Foreign Minister Sergei Lavrov in New York.
Ukraine and its allies have pressed for a moratorium in attacks on energy infrastructure and for guarantees on Black Sea shipping, fearing Russian forces could target power and heating facilities during the northern hemisphere winter.
"I think both sides have expressed an interest in some limited ceasefire that involve grain and energy. Obviously, you know, that won't be easy either," Rubio told reporters.
Russia has given no public indication it is ready to agree to such arrangements, and it was not immediately clear whether Rubio was suggesting movement in his talks with Lavrov.
Rubio said it was a particular challenge that energy strikes were at the core of both countries' tactical priorities in their war, which is now in its fifth year.
Addressing the 15-member Security Council on the sidelines of the annual United Nations gathering of world leaders, Lavrov indicated Russia would not countenance any temporary cessation of hostilities.
"Europe, whatever it thinks, just wants to get a pause, and it wants to use it to pump the Kyiv regime with weapons," he told a council session focused on the war in Ukraine.
The United Kingdom, France and Denmark's top diplomats used their speeches to deliver strong condemnations of Russia's war, warning variously of dangerous escalation and the spike in civilian deaths.
with EFE and DPA
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