More than 50 Ukrainian POWs were killed when a prison in the frontline town of Olenivka was struck by rockets on Friday.
Both sides are blaming each other for the strikes.
Russia claims the attack was carried out by Ukrainian forces using high-precision US-made Himars artillery, which Kyiv denies.
Ukraine said Russia carried out the attack to cover up evidence of war crimes.
Moscow published footage of what it said was the camp after the attack took place.
The unverified video shows a destroyed building with damaged bunk beds and badly burnt bodies.
The exact details of what happened at the camp, controlled by the Russian-backed separatists in the Donetsk People’s Republic, remain unclear.
Mr Zelenksy joined his foreign minister, Dmytro Kuleba, in calling for the Red Cross and United Nations to intervene and investigate.
The prisoners detained at the facility – many of which are believed to have been captured while defending the Azovstal steel plant in Mariupol – should have been protected by guarantees secured by both the organisations.
“It was a deliberate Russian war crime, a deliberate mass murder of Ukrainian prisoners of war,” Mr Zelensky said.
“Russia has proven with numerous terrorist attacks that it is the biggest source of terrorism in today’s world.”
The Red Cross said it had requested access to the prison so that it can help evacuate and treat the 130 POWs Ukraine said were wounded by the attack.
Russia put the number of wounded at 75 and the figure dead at 40.
The Red Cross said in a statement: “Our priority right now is making sure that the wounded receive life-saving treatment and that the bodies of those who lost their lives are dealt with in a dignified manner.
“We have requested access to determine the health and condition of all the people present on-site at the time of the attack. We are also in contact with families, taking their requests and inquiries.
“All prisoners of war, wherever they are held, are protected under international humanitarian law. They are no longer part of the fight and should not be attacked. The ICRC has been able to visit some POWs and other detainees, but it hasn’t been granted access to visit them all.”
Ukraine’s new prosecutor-general, Andriy Kostin, said he had ordered officials to open up a war crimes investigation into the killings.