Zelenskiy said Russian forces used ballistic missiles supplied by North Korea in their overnight attack on the southeastern Ukraine city of Zaporizhzhia, where local officials said six people were killed and 19 wounded.
A further three people, including a 15-year-old boy, were killed by Russian drones and artillery in the central Dnipropetrovsk region, local authorities said.
Russia had received additional ballistic missiles from Pyongyang and was preparing to deploy more North Korean troops, Zelenskiy said late on Monday.
Russian President Vladimir Putin and North Korean leader Kim Jong-un signed a strategic partnership agreement just over two years ago.
Kim has sent thousands of troops and huge supplies of weapons to support Putin's invasion of Ukraine.
Some experts say the engagement with Moscow is helping improve North Korea's military capabilities, and Zelenskiy warned the battlefield experience would help Pyongyang menace other countries in its region.
Ukraine says Russia is scaling up its production of ballistic missiles, aiming to exploit Kyiv's critical shortage of Patriot air defence interceptors that can stop them, and claims Moscow is readying an increase in recruitment for a new push on the front line that stretches 1250km along eastern and southern Ukraine.
"Every step Russia takes - increasing ballistic missile production, bringing in North Korean equipment, preparing for mobilisation - all of this shows that Moscow is preparing not for peace, but for escalation," Zelenskiy said on social media on Tuesday.
US-led diplomatic efforts to stop the war have fizzled as Washington grew frustrated with the lack of progress towards a settlement and its attention turned to the Iran war.
"The Kremlin will not enter serious negotiations or make meaningful compromises on its demands as long as Putin believes that he has a viable military path to achieving his full objectives," the Institute for the Study of War, a Washington-based think tank, said in an analysis on Monday.
Russian forces also struck parts of the Ukrainian capital, Kyiv, overnight, according to officials.
One strike hit the grounds of a children's hospital, leaving two craters and shattering windows, the State Emergency Service said.
Children and medical workers were in bomb shelters and nobody was hurt, it added.
At another location in the capital, a Russian strike started a fire in a warehouse that spread across about 1200 square metres, according to emergency officials.
The Russian defence ministry said its forces overnight struck "military industrial facilities and transport and logistics centres" in Kyiv and Zaporizhzhia with "ground-based precision weapons".
It said on Tuesday that it hit drone storage facilities in Kyiv and a metallurgical plant in the city of Zaporizhzhia.
Russia targeted Zaporizhzhia and Kyiv with Zircon anti-ship missiles and Iskander ballistic missiles, while launching 120 long-range strike drones of various types across the country, Ukraine's air force said.
Meanwhile, the Russian defence ministry said its air defences overnight intercepted almost 400 Ukrainian drones over 14 Russian regions and occupied Crimea.
Russia's biggest online retailer, Wildberries, said its logistical facilities in the Voronezh region on the border with Ukraine came under attack and caught fire, but it said the fire has been extinguished.
It said goods stored at the facilities were "largely undamaged".
Ukraine has repeatedly struck Wildberries warehouses and has also bombarded Russian oil facilities in what it says is a strategy to compel Putin to negotiate an end to the invasion.
