Kyiv also said Russian shelling killed one person on New Year’s Day in the southern Odesa region and another person in Kherson, also in the south.
The barrage came after Russia pounded Ukraine in the last days of 2023, killing 39 people in one of the biggest strikes in the war.
Ukraine’s air force said Russia launched 90 Iranian-made Shahed drones on the last night of the year.
“On New Year’s Eve, the defenders of the sky managed to destroy a record number of enemy attack drones — 87 out of 90,” the air force said.
It said Moscow also launched missiles in the northeastern Kharkiv region, Kherson and Zaporizhzhia in the south.
Odesa was shelled on New Year’s Eve, Kyiv said, with emergency services reporting one person killed. A 73-year-old woman was killed in Kherson in shelling.
The drone attacks also targeted the western city of Lviv near the Polish border.
Lviv Mayor Andriy Sadovy said a university linked to a Ukrainian nationalist figure and a museum were damaged.
Russia, meanwhile, reported Ukrainian drone attacks on its Belgorod region near the border.
Moscow and Kyiv have escalated attacks in recent days, with an unprecedented Ukrainian attack on the city of Belgorod killing 24 people on Saturday.