"A missile shot down near Kyiv," the city's mayor Vitali Klitschko said on the Telegram messaging channel. "Air defence working!"
Monday's blasts were heard in several districts of the city, including Kyiv's historic neighbourhood of Podil, where falling debris damaged a roof on a house, he said.
According to preliminary information from officials, there were no casualties in the overnight attacks.
The attack, appearing to be a combination of missile and drones, follows the largest drone barrage launched on Kyiv on Sunday, which killed one person and injured several. Waves of attacks now come several times a week.
The full scale of the latest attack was not immediately known. Reuters witnessed said they heard several loud blasts when the city and all of Ukraine were under air raid alerts.
With a long-promised Ukrainian counteroffensive looming to recapture territory taken by Russia in the 15th months of the war, Moscow has intensified its attacks, targeting military infrastructure and supplies.
While Ukraine almost never publicly claims responsibility for attacks inside Russia, a series of strikes inside the country have targeted military, energy and transport infrastructure, with Moscow blaming Kyiv for the attacks.
Kyiv celebrates founding day
Despite heavy air strikes before dawn on Sunday, crowds poured into the streets later on to celebrate the anniversary of the founding of Kyiv 1541 years ago.
Ukrainian military said it had downed 58 of the 59 launched drones, described by the air force as a record assault with the Iranian-made "kamikaze" drones. President Volodymyr Zelenskiy said all 36 drones targeting Kyiv had been destroyed.
"This is how Russia celebrates the day of our ancient Kyiv," Zelenskiy said in his nightly address.
Residents emerged from shelters to attend live concerts, sample food stalls and enjoy craft shows in festivities that were scaled down from previous years.
"Strength is in people, it is in cities, it is in life, and when life, people, and the most important cities for culture are despised, Russia will only face defeat," Zelenskiy said.
Moscow did not comment on the attacks. Separately, Russian media cited Kremlin spokesman Dmitry Peskov as reiterating that Moscow's goals in Ukraine will be achieved.
Several districts of Kyiv, by far the largest Ukrainian city with a population of about 3 million, suffered in the overnight attacks, officials said, including the historical Pecherskyi neighbourhood.
Falling debris killed a 41-year-old man, the mayor said, while several other people were injured.
Reuters witnesses said that during the air raid alerts that started soon after midnight, many people stood on their balconies, some screaming offensives directed at Russia's President Vladimir Putin and "Glory to air defence" slogans.
France condemned the attack "in the strongest terms", adding that it had claimed the lives of at least two people and left several injured, in what it called a flagrant violation of international humanitarian law. "These unacceptable acts constitute war crimes and cannot go unpunished," the French foreign affairs ministry said in a statement.
LOOMING COUNTER-OFFENSIVE
Ukraine's Air Force said that Russia had targeted military and critical infrastructure facilities in central Ukraine on Sunday, and the Kyiv region in particular - as has been increasingly the case with a Ukrainian counteroffensive looming.
Zelenskiy said one drone hit an unidentified infrastructure target in the Zhytomyr region, west of the capital.
Ukrainian Air Force spokesperson Yuri Ihnat told Ukrainian television that a combination of fighter aircraft and mobile air defence systems were used to down the drones but did not say what systems were deployed. He has said previously that Ukraine uses the NASAMS air defence systems to destroy the Shahed drones.
On Saturday, Ukraine's Air Force thanked the United States for sending more of the NASAM systems, among others, as well as the US-made Stinger portable systems also used for downing drones, that were part of the US aid package in April.
The expensive Patriots systems, Ihnat said on Sunday, have made air defences more effective and have been used chiefly for more sophisticated weaponry, such as Russia's hypersonic Kinzhal missiles.
Reuters was unable to independently verify the information on what systems were used or how many drones were launched and destroyed.
The Sunday attacks came after Kyiv said that combat clashes eased around the besieged city of Bakhmut in southeastern Ukraine, the site of the war's longest battle.
Serhiy Cherevatyi, spokesman for Ukraine's eastern military grouping said only one military clash had occurred in Bakhmut over the past 24 hours, though Russian forces maintained heavy artillery strikes.
Over the weekend, Kyiv indicated that its forces were ready to launch a long-promised counteroffensive to recapture territory taken by Russia in the 15 months of the war.
"Throughout its history, Kyiv has seen various meanness from invaders. It has survived them all, and it will survive the (Russians)," Zelenskiy said on Sunday.
