The message came from the Ukrainian authority responsible for handling and coordinating issues related to prisoners of war and the fallen.
According to the authority in Kyiv, it concerned 909 fallen soldiers whose remains were returned to Ukraine.
Russia has not commented on the latest exchange.
On March 28, Ukraine received the remains of 909 soldiers in an exchange where Russia received 43 fallen Russian soldiers, according to Russian state media.
Prisoner exchange and handover of remains is one of the few areas where functioning talks are ongoing between attacking Russia and Ukraine.
The number of soldiers who have fallen on both sides in the Russian war of aggression is not officially established. In an interview with the American TV company NBC in mid-February, President Volodymyr Zelensky said that over 46,000 Ukrainian soldiers had fallen and around 380,000 had been injured.
Calculations according to the British BBC and the Russian, independent media organization Mediazona have identified around 100,000 Russian soldiers who have fallen since the invasion on February 24, 2022, and have been named through scrutiny of Russian open sources.