He accused Moscow of carrying out brutal and senseless bombing and shelling of Ukrainian cities as it intensified its offensive.
"This is a deliberate and criminal attempt to kill as many Ukrainians as possible and destroy as many houses, social facilities and enterprises as possible," Zelensky said in a video address late on Thursday.
"This is what will be qualified as the genocide of the Ukrainian people and for which the occupiers will definitely be brought to justice," he added, as cited by the ukrinform.net website.
He also said in his message that "the first trial in Ukraine against a Russian war criminal has already begun" and that his country "will find and bring to justice all those who give and carry out criminal orders."
Zelensky has previously said that more than 500,000 Ukrainians have been deported to Russia by force, and that tens of thousands of people were being held in Russian camps.
Source: PAP, ukrinform.net, Reuters