Ukraine and Russia have held two rounds of talks in Istanbul over the past five months.
They have agreed to swap prisoners but made no breakthroughs in ending almost three and a half years of conflict that started with Russia's 2022 invasion.
"Everything should be done to achieve a ceasefire," Zelenskiy said in his nightly video message.
"The Russian side should stop hiding from decisions," he added.
"Ukraine is ready for such a meeting."
The president said Rustem Umerov, who headed the Ukrainian delegation at both talks in Istanbul, had sent the Russian side the offer to hold the meeting next week but gave no more details.
Umerov, a former defence minister, was appointed last week as the head of the National Security and Defence Council and tasked with adding more momentum to the negotiations.
Russia has been pressing a grinding offensive along the eastern front in Ukraine's Donetsk region.
It has repeatedly said it is ready for a new round of talks but has not backed down from what Ukraine and its allies describe as its maximalist war aims.
US President Donald Trump, who has sharpened his tone against Russia in recent weeks amid worsening air strikes on Ukrainian cities, threatened harsher sanctions on Russia earlier this month if a peace deal was not reached within 50 days.
Earlier on Saturday, Moscow mayor Sergei Sobyanin said Russian air defence systems had shot down three drones en route to the capital.
Two Moscow airports - Vnukovo and Domodedovo - suspended arrivals and departures for safety reasons but later resumed operations, Russian aviation watchdog Rosaviatsia said.
The Russian Defence Ministry said its air defence systems intercepted and destroyed 27 Ukrainian drones in total from 3pm to 7pm Moscow time, including four over Moscow region, 15 over Bryansk region, six over Kaluga region and two over Tula region.
Zelenskiy said Russian forces had launched attacks involving more than 300 drones and about 30 missile and cruise missiles on Ukrainian cities the previous night.
Zelenskiy posted photos on Telegram showing damage caused to a residential block in Odessa on the Black Sea, where one person was killed and six others injured, according to local officials.
Two people were killed in a Russian missile strike in the Synelnykove district, the military governor of the Dnipropetrovsk region Serhiy Lysak said.
The Donetsk, Kherson and Zaporizhzhia regions were also hit, according to Zelenskiy.
with AP and DPA
8°C