"This summer Russia is preparing something there, under cover of military exercises," Zelenskiy told a summit in Warsaw, without giving details or citing evidence.
Russia and Belarus have announced joint military drills for September.
Russian troops were trying to carve out a buffer zone in Ukraine's northeastern Sumy region although so far without substantial success, the regional governor said on Tuesday.
The Sumy region borders on Russia's Kursk region, where Russian forces have lately recaptured territory seized last year in the Ukrainian military's only major cross-border incursion of the war.
Ukraine has said for months that it is concerned about Russian troops trying to advance into Sumy.
Russia has said its forces have captured some territory there and have driven all Ukrainian troops out of Kursk.
Sumy Governor Oleh Hryhorov said on the Telegram app that four border villages in Sumy - Zhuravka, Veselivka, Basivka and Novenke - were in a "grey zone" due to Russian attacks but were not under Russian control.
"Currently, the enemy continues to try to carve out a buffer zone on the territory of our region but has not had any significant success," Hryhorov said.
Of the four villages, he said "there is no question of their occupation at the moment".
Russia's defence ministry said earlier in April that its forces had captured Zhuravka and Basivka, which Ukraine denied.
DeepState, an open source map compiled from observations of the battlefield, says about 52 square kilometres of the Sumy region are in a contested grey zone.
Meanwhile, US Secretary of State Marco Rubio said the time has been reached for concrete proposals from Russia and Ukraine to end the war, State Department spokeswoman Tammy Bruce said on Tuesday.
If there is no progress the United States will step back as a mediator, she added.
"We are now at a time where concrete proposals need to be delivered by the two parties on how to end this conflict. How we proceed from here is a decision that belongs now to the president. If there is not progress, we will step back as mediators in this process," Bruce said, citing a statement from Rubio, and referring to US President Donald Trump.
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