Andrii Nebytov, chief of Kyiv's police, posted a photo on his Telegram messaging app, showing what was described as a piece of drone used in an attack on the capital, with a hand-written sign on it in Russian saying "Happy New Year".
"This wreckage is not at the front, where fierce battles are taking place, this is here, on a sports grounds, where children play," Nebytov said.
Russia has flattened Ukrainian cities and killed thousands of civilians since Putin ordered his invasion in February, claiming Ukraine was an artificial state whose pro-Western outlook threatened Russia's security. Moscow has since claimed to have annexed around a fifth of Ukraine.
Ukraine has fought back with Western military support, driving Russian forces from more than half the territory they seized. In recent weeks, the front lines have been largely static, with thousands of soldiers dying in intense trench warfare as Moscow defends its grip on captured territory.
Since October, Russia has launched mass missile and drone attacks on Ukraine's energy infrastructure, casting cities into darkness and cold as winter sets in. Moscow says the strikes aim to reduce Ukraine's ability to fight; Kyiv says they have no military purpose and are intended to hurt civilians, a war crime.
"The main thing is the fate of Russia," a stern-faced Putin said in his New Year's Eve address, speaking in front of a group of people dressed in military uniform instead of the normal backdrop of the Kremlin walls. "Defence of the fatherland is our sacred duty to our ancestors and descendants. Moral, historical righteousness is on our side."
Zelensky delivered his own address in near darkness, in front of a fluttering Ukrainian flag. He described the year past as a national awakening.
"We were told: you have no other option but to surrender. We say: we have no other option than to win," he said.
"This year has struck our hearts. We've cried out all the tears. We've shouted all the prayers," Zelensky said. "We fight and will continue to fight. For the sake of the key word: 'victory'."
The latest air strikes damaged infrastructure in Sumy, in the northeast of the country, Khmelnytskyi in the west and Zaporizhzhia and Kherson in southeast and south, the General Staff of Ukraine's Armed Forces said.
"Let the day be quiet," Valentyn Reznichenko, governor of the Dnipropetrovsk region said early on Sunday, after reporting heavy shelling of several communities in the region overnight that wounded one.
Grid operator Ukrenergo said on Sunday the past day had been "difficult" for its workers but that the electricity situation was "under control" and emergency outages were not being implemented.
"Additional volumes of electricity for household consumers have been provided thanks to the concious behavior of Ukrainian business and restrictions on the work of industry," it said in a statement.
Separately, Vyacheslav Gladkov, governor of the southern Russian region of Belgorod bordering Ukraine, said overnight shelling of the outskirts of Shebekino town had damaged houses but there were no casualties.
Russian media also reported multiple Ukrainian attacks on the Moscow-controlled parts of the Donetsk and Luhansk regions, with local officials saying at least nine people were wounded.
Russia's RIA state news agency cited a local doctor as saying six people were killed when a hospital in Donetsk was attacked on Saturday. Proxy authorities in Donetsk also said one person had been killed by Ukrainian shelling.
Reuters could not verify the reports. There was no immediate response from Kyiv, which almost never publicly claims responsibility for any attacks inside Russia or on Russian-controlled territories in Ukraine.
