A series of powerful explosions shook the capital around early Wednesday local time as local officials said air defences were working to thwart the attacks.
"This Russian terror against Ukraine will not stop on its own," Ukrainian President Volodymyr Zelenskiy said after the attack, urging unity among partners for a just end to the war.
"Putin is not preparing for peace - he continues to kill Ukrainians and destroy cities."
Prospects for renewed peace negotiations to end the war that Russia launched on Ukraine nearly three years ago have increased after US President Donald Trump said he had been in contact with Kyiv and Putin.
Zelenskiy also said on Tuesday that Kyiv would soon hold talks with US officials.
Ukraine's air force said it shot down six out of seven ballistic missiles launched in the attack. Out of 123 drones, the military shot down 71 and likely used electronic countermeasures against 40 more.
Local officials on the Telegram app said that at least one person was killed and four injured, including a nine-year-old child, in the attack on Kyiv.
The attack caused damage in Kyiv's Holosiivskyi, Podilskyi, Sviatoshynskyi and Obolonskyi districts, Kyiv mayor Vitali Klitschko said on Telegram.
Earlier, Zelenskiy said he will offer to swap land Ukrainian troops control in Russia's Kursk region in exchange for a return of Ukrainian territories Russia occupies if negotiations take place.
"We will swap one territory for another," Zelenskiy said in an interview with The Guardian.
Zelenskiy did not specify the Ukrainian territories he would ask for.
"I don't know, we will see. But all our territories are important, there is no priority," he added.
Russia occupies about 20 per cent of Ukrainian territory in the country's east and south as the full-scale invasion it launched on February 24 approaches its third anniversary.
Ukraine staged a surprise offensive into the Kursk region of western Russia last August and still occupies part of the initially captured territory, although its size has dwindled in the course of Russian counter-attacks.
Ukrainian officials say the Kursk operation was meant to protect border regions and that captured land could be used as a bargaining chip in any peace negotiations, whose prospects have risen since Donald Trump returned as US president.
Zelenskiy has repeatedly stressed that any plan to end the war in Ukraine should provide for strong security guarantees from allies to ensure no future Russian aggression is possible.
Trump said he would probably meet Zelenskiy this week to discuss ending the war.
He indicated on Sunday that he had been in contact with Putin, without specifying when.
The Kremlin neither confirmed nor denied those contacts.
Sappers from Russia's Emergency Situations Ministry defused a downed French-made SCALP cruise missile in the Kursk region, the ministry said on Tuesday.
Trump wrote in a social media post on Tuesday that US Treasury Secretary Scott Bessent will travel to Ukraine this week.
Bessent, who will be the first cabinet-level official in Trump's administration to visit Ukraine, is set to discuss potential US access to Ukraine's rare earth mineral resources, according to one source with knowledge of the matter.
Both Zelenskiy and Trump have expressed interest in a pact in which the United States wourld receive rare earths from Ukraine in exchange for continued support in fending off invasion from Russia.
A number of other US officials travelling to Europe this week will discuss the Ukraine war.
They include Secretary of State Marco Rubio, Vice President JD Vance, Defence Secretary Pete Hegseth and Keith Kellogg, the US special envoy for Ukraine.
Rare earths are a group of metals used to make magnets that turn power into motion for electric vehicles, mobile phones, missile systems and other electronics.
There are no viable substitutes and demand is widely expected to grow.
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