In a post on social media, President Zelensky said Ukraine’s Dnipropetrovsk, Mykolaiv, Chernihiv, Zaporizhzhia, Poltava, Kyiv, Odesa, Sumy and Kharkiv regions were attacked by Russia overnight.
He said “residential areas and civilians facilities” were hit.
In the central city of Dnipro, the president added, there was a “direct hit of a missile with cluster munitions on a high-rising residential building”.
The BBC has verified footage uploaded this morning showing a missile in flight and an impact, as well as still images of a badly damaged building in the same location in Dnipro.
In Russia, Samara regional Governor Vyacheslav Fedorishchev said four people were killed “as a result of an overnight attack by enemy drones”.
He said that another person was injured, without giving any other details.
Ukraine’s military said its drones struck the Novokuibyshevsk oil refinery in the Samara region. It also said the Saratov oil refinery was hit overnight in the neighbouring region.
Cross-border drone raids have become a prominent feature of the war. In July, a sustained Ukrainian drone attack forced the temporary closure of all of Moscow’s airports.
Kyiv has been systematically targeting Russian oil and other key industrial facilities, which play a key role in Russia’s continuing war effort in Ukraine.
Meanwhile, Moscow has in recent weeks escalated its aerial assaults on Ukraine, while Kyiv and its Western allies – including the US – continue to call for a ceasefire.
Earlier this month, the main government building was hit in Ukraine’s capital Kyiv by what Ukraine said was a Russian Iskander cruise missile.
Zelensky said on Saturday that he planned to meet US President Donald Trump on the sidelines of the United Nations General Assembly (UNGA), taking place in New York next week.
Trump hosted Russian President Vladimir Putin in Alaska last month, hoping to secure a deal on ending the conflict. No such agreement was made.
Putin launched a full-scale invasion of Ukraine in 2022.
The latest Russian aerial attack comes a day after Estonia requested urgent consultations with other Nato members after Russian jets violated its airspace – staying there for 12 minutes before being intercepted.
Russia denied violating Estonian airspace.
Tensions have been escalating recently after Poland and Romania – both Nato members – said Russian drones breached their airspace earlier this month.