Ukrainian President Volodymyr Zelensky has told Russians that their leader is destroying their country.
Speaking after Vladimir Putin delivered a New Year address flanked by people in military uniform, Mr Zelensky said the Russian president was hiding behind his troops, not leading them.
Saturday saw a day of deadly strikes across Ukraine, and Mr Zelensky said Ukrainians would not forgive Russia.
At least one person died and dozens were injured in the attacks.
The head of Ukraine's armed forces, Valerii Zaluzhny, said air defences had shot down 12 of 20 Russian cruise missiles on Saturday.
There were further missile strikes on Kyiv just hours into the New Year on Sunday, officials said. The Ukrainian Air force said it had shot down 45 Iranian-made kamikaze drones overnight.
But the strikes, which came in the opening hours of 2023, fuelled anger and hate among Ukrainians already tired of Russia's unrelenting air campaign.
As explosions rocked the capital, some residents sang the national anthem, while officials accused Russia of deliberately targeting civilians while they gathered to celebrate the New Year.
Andriy Nebitov, the head of the Kyiv police, posted an image to social media of a downed drone with the words "Happy New Year" scribbled across it in Russian.
"That is everything you need to know about the terror state and its army," he wrote on Facebook, adding that the remains had crashed in a children's playground.
The latest wave of attacks happened two days after one of the largest air strikes since the start of the war. Dozens of attacks in recent weeks have caused repeated power cuts.
Moscow has repeatedly denied targeting civilians, but Mr Putin has recently admitted hitting critical energy facilities.
In an address on his Telegram channel, Mr Zelensky said those who carried out Saturday's attacks were inhuman.
Switching from Ukrainian to Russian, he then attacked Mr Putin.
"Your leader wants to show you that he's leading from the front, and his military is behind him," he said.
"But in fact he is hiding. He's hiding behind his military, his missiles, the walls of his residences and palaces.
"He's hiding behind you, and he's burning your country and your future. No one will forgive you for terror. No one in the world will forgive you for that. Ukraine will not forgive."
Mr Zelensky later gave a new year's address to the Ukrainian people, thanking them for their "incredible" efforts in repelling Russian advances.
"We fight as one team - the whole country, all our regions. I admire you all. I want to thank every invincible region of Ukraine," he said.
Mr Putin also issued a new year address which was broadcast for each of Russia's 11 time zones as they saw in 2023.
The Russian leader tried to rally people behind his troops fighting in Ukraine, saying the country's future was at stake.
In combative mood, Mr Putin said: "We always knew, and today it is confirmed to us yet again, that a sovereign, independent and secure future for Russia depends only on us, on our strength and will."
He presented the invasion of Ukraine's sovereign territory as "defending our people and our historical lands" and said "moral, historical rightness is on our side".
Mr Putin also accused the West of "provoking" Moscow to launch its invasion of Ukraine on 24 February.
"The West lied about peace. It was preparing for aggression... and now they are cynically using Ukraine and its people to weaken and split Russia," he said.
Ukraine and the West reject Russia's claims about the start of the aggression.
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