"Dozens of people have been injured, including a child. As it stands now, two people have been reported dead," Zelenskyy wrote on X.
According to Zelenskyy, the Sumy, Odesa and Kharkiv regions were among those attacked.
Earlier on Sunday, Kharkiv Mayor Ihor Tereshov said a woman in her 20s was killed and several others injured in a Russian drone strike. The attack in the early hours was reported to have targeted a private residence, AFP writes.
Zelenskyy thanked everyone who is working "around the clock" to restore electricity, heating and water after recurring Russian attacks.
Ukrainian negotiators arrived in the United States on Saturday for new talks with US envoys Steve Witkoff and Jared Kushner. Sunday's meeting is expected to focus on security guarantees and post-war recovery.
