Zelenskiy, speaking in his nightly video address, suggested the new attack could occur on Monday, but gave no further details of a time frame or possible targets.
"Please pay attention to air raid alerts today. Intelligence indicates that Russia may be preparing a massive strike," he said.
"Relevant orders for air defence have already been issued."
Russian forces have regularly staged air strikes on Ukrainian towns and cities, mainly at night and including the capital Kyiv.
Energy infrastructure has been a repeated target.
Russian forces have suffered thousands of dead and seriously wounded soldiers at the start of their northern hemisphere spring offensive in Ukraine over recent weeks, Ukraine's top military officer Oleksandr Syrskyi said on Facebook on Monday.
"Within four days, the enemy has lost more than 6090 soldiers as fallen or wounded," the four-star general said.
Russian casualties over the past week had totalled more than 8700 dead and seriously wounded, Syrskyi said.
They had nevertheless failed to break through along the front, the commander-in-chief said.
His information could not be independently verified.
Observers have seen increased activity by Russian units along the front in recent days, with Russian troops attempting to exploit improved weather conditions and the end of the muddy period to increase their attacks.
The Russian defence ministry for its part has reported taking two more localities in the eastern Donetsk region.
It says that Russian forces are constantly improving their positions in eastern Ukraine.
with DPA
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