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.