They say this was part of a swap with Russia, with each side receiving 160 bodies. Moscow has not commented.
On the Ukrainian side, more than 50 bodies were those of members of the Azov regiment, the families say.
The Ukrainians were holed up in the Azovstal steelworks for weeks. In May, the survivors were taken prisoner.
Kyiv says Mariupol's last defenders were given orders to save their lives after successfully completing their main goal of holding up Russian troops and not allowing them to be redeployed to other key battlefields.
