President Volodymyr Zelensky vowed to wreak "wrath" against Russian forces in 2024, hours before Ukraine saw attacks on the first day of the year.
Russia and Ukraine have seen an escalation in strikes in recent days, including an unprecedented assault on the Russian city of Belgorod that killed 24 people on Saturday.
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The attack came a day after Moscow launched a barrage of missiles and drones at Ukrainian cities, killing 39 people in one of the biggest aerial attacks since the war began.
January 1 is a day of mourning in Ukraine's capital Kyiv, where 27 people had been killed, city officials said.
Just hours after midnight on New Year's Day, the Russian-installed head of the occupied Donetsk region said four people had been killed and 13 wounded in "massive shelling" from rockets on its main city.
In Ukraine's southern Odesa region, governor Oleg Kiper said one person died in a Russian drone attack, and three others were wounded.
And in western Ukraine's Lviv region, air defence systems shot down Russian drones in Monday's early hours, according to governor Maksym Kozytskyi.
Zelensky's televised New Year's address featured clips of Ukrainian artillery and fighter jets.
"Next year, the enemy will feel the wrath of domestic production," Zelensky said.
Ukraine will have at least "a million" additional drones in its arsenal next year, Zelensky added, as well as F-16 fighter jets delivered by its Western partners.
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"Our pilots are already mastering F-16 jets, and we will definitely see them in our skies," he said.
Despite billions of dollars worth of Western weapons, Ukraine struggled to make a major breakthrough in its 2023 counteroffensive against invading Russian forces.
Moscow has meanwhile ramped up pressure along the frontlines, capturing the eastern town of Marinka earlier in December and pushing for control of Kupiansk in the northeast.
Ukraine is urging Western allies to maintain military support.
Britain announced it would send hundreds more air-defence missiles to Kyiv, after Prime Minister Rishi Sunak declared: "We must continue to stand with Ukraine -- for as long as it takes."
Zelensky's counterpart President Vladimir Putin did not mention Ukraine in his traditional New Year's Eve address on Sunday, but praised Russia's soldiers on the front line and called for unity in the face of "difficult tasks".
"To all those who are on duty, on the front line of the fight for truth and justice," Putin said, "you are our heroes. Our hearts are with you. We are proud of you, we admire your courage."
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