KYIV -- Russia has continued its rocket and drone onslaught against Ukraine, with New Year's Day blasts killing at least three civilians and wounding dozens of others, while Kyiv said its forces had inflicted "heavy" losses on Russian-backed separatist fighters around the strategic eastern city of Bakhmut.
Attacks late on December 31 and early on January 1 were reported in the capital, Kyiv, and other cities, including in the city of Khmelnytskiy, where officials said a 22-year-old woman died from injuries suffered in a Russian rocket attack the day before.
In his New Year's address, Ukrainian President Volodymyr Zelenskiy maintained his defiant tone amid the relentless Russian attacks, telling the Ukrainian people that "I want to wish all of us one thing -- victory."
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Ukraine's military early on January 1 said its defense forces had shot down at least 32 Iranian-made drones since midnight on top of the 13 others destroyed on the night of December 31.
Ukrainian presidential aide Kyrylo Tymoshenko said two civilians were killed in the capital as a result of Russian strikes on January 1 in addition to the woman in Khmelnytskiy.
On December 31, Ukraine reported that at least 43 missile and air strikes across the country had killed one person and wounded at least 50.
In the capital, Andriy Nebytov, head of the regional police, posted a photo on Facebook that he said showed wreckage of Iranian-made drone with the words "Happy New Year" in Russian written on it.
"Here it is -- part of the night's greetings from the 'brotherly people' on the New Year!" he said in the post. "Cheap and tasteless!"
Late on January 1, the Ukrainian military said it inflicted heavy losses on Russia's troops around Bakhmut, the site of intense fighting in recent months as Moscow attempts to take the town from Kyiv's forces.
Serhiy Cherevatiy, a Ukrainian military spokesman, told Ukrainian television that some 170 Russian soldiers were killed and 200 wounded in fighting for control of the town on December 31, labeling it a "conveyor belt of death" for Russia's troops.
Cherevatiy did not comment on Ukrainian casualties.
Strikes were also reported in the southern port city of Kherson, where officials said a children's hospital came under attack.
In a Facebook post, the Kherson regional administration said that "in the first minutes of the new year, Russia launched another terrorist strike -- the enemy fired about seven shells at the Kherson Regional Children's Clinical Hospital."
It added that there were no casualties but that 17 children, four parents, and 38 staff members were evacuated.
Russian forces retreated from Kherson in November after a powerful Ukrainian counteroffensive, but they continue to shell the city, forcing many of the residents who returned home to flee once again.
Moscow denies that it targets civilian sites in the war, despite evidence to the contrary.
Meanwhile, Russian occupation authorities in the Donetsk region said shelling by Kyiv's forces had killed a man and a woman in the town of Yasynuvata, Reuters reported.
Battlefield claims on either side cannot immediately be confirmed.
WATCH: Russian cruise missiles damaged residential buildings in Kyiv and several other cities on December 31.
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Russia Hits The Ukrainian Capital With Missiles On New Year’s Eve
In his midnight address, Russian Vladimir Putin said that "moral, historical rightness is on our side," even as international condemnation intensifies and amid unexpected battlefield setbacks.
Russian authorities claimed on January 1 that their forces had targeted "the facilities of the military-industrial complex of Ukraine."
"The aim of the strike was achieved," a military statement said.
Ukrainian officials also said on January 1 that Russia had used missile carriers located in the Caspian Sea to launch rockets toward Ukraine.
Natalya Humenyuk, the head of the joint coordination press center of the defense forces in southern Ukraine, said that "this is probably because it has become more difficult for them to deliver their reserves to the Black Sea coast" due to Ukrainian efforts to keep Russian naval forces under pressure in the Black Sea.