"Investigators have already documented more than 400 Russian war crimes," Zelensky said in a video address late on Sunday, as cited by the ukrinform.net website.
He added that "the bodies of both civilians and military personnel" were "being found."
He vowed: "We will find and bring to justice every murderer. Without a doubt."
Zelensky also said that "stabilization and restoration of law and order in 226 settlements will be ensured in the Kherson region."
He added that "the situation in the Kherson region is still very dangerous. First of all, there are mines. Unfortunately, one of our sappers died, and four others were injured while clearing mines."
He announced that Russian soldiers and mercenaries were being detained, accompanied by the "neutralization of saboteurs."
Fighting in Donetsk region remains intense: Zelensky
Zelensky also said in his message that fighting in eastern Ukraine's Donetsk region remained "as intense as in previous days," with "the level of Russian attacks not decreasing."
He said: "The level of resilience and bravery of our fighters is the highest. We do not allow our defense to be breached."
He reported that five Ukrainian regions, Sumy, Kharkiv, Zaporizhzhia, Luhansk, and Donetsk, were hit by Russian missile, air and artillery strikes on Sunday.
"We do everything to make the enemy feel our retaliation," he stated. "To the maximum."
He added, as quoted by the president.gov.ua website: "Along the entire frontline, we ensure the destruction of enemy supply chains, ammunition depots, and enemy headquarters."
Zelensky last Friday announced the liberation of the southern city of Kherson after Russian forces withdrew from the area earlier that day.
Source: IAR, PAP, Reuters, ukrinform.net, ukrinform.net, president.gov.ua