Ukraine said it received 1000 bodies and Russian state news agency TASS quoted an unidentified source as saying Russian authorities were given back 30.
"Investigators from law enforcement bodies, together with expert agencies of the Ministry of Internal Affairs, will soon conduct all necessary examinations and identify the repatriated bodies," Ukraine's prisoner-of-war co-ordination centre said on Telegram.
It thanked the Red Cross for its mediation.
Amid continuing military exchanges, Ukraine and Russia have repeatedly exchanged the bodies of the deceased, and this is the 15th such exchange this year.
Ukraine has received the bodies of more than 15,000 soldiers in these exchanges.
The slow Russian advance has meant that Russia returns more bodies than Ukraine does.
The two sides have also exchanged live prisoners in the course of the war that began with Russia's full-scale invasion of Ukraine on February 24, 2022.
But peace talks remain stalled and negotiators from the two sides have not publicly met face-to-face since July 23, when they talked for just 40 minutes in Istanbul.
European countries pushed back on Thursday against a US-backed peace plan for Ukraine that sources said would require it to give up more land and partially disarm, conditions long seen by Ukraine's allies as tantamount to capitulation.
Ukraine has previously accused Russia of returning bodies in a disorderly way, and of sometimes sending the bodies of Russian soldiers.
Russian authorities have denied this.
Ukraine's military said on Thursday it had struck Russia's Ryazan and Ilsky oil refineries.
Ukraine's military general staff said it had struck the Ryazan refinery overnight, recording a hit and observing fires in the vicinity of secondary oil processing facilities.
Ukraine had also hit this refinery in a previous strike last week.
Separately, Ukraine's drone force chief Robert Brovdi said the Ilsky refinery had been struck by his units the night before.
More than 400,000 Ukrainian consumers remained without electricity as of midday on Thursday following a recent Russian attack on Ukraine's western regions, energy officials said.
The attack led to a decrease in electricity production at Ukrainian nuclear power plants.
Ukraine generates more than half of its electricity at three nuclear power plants but damage to power lines and transformers has forced the plants to reduce their output, a representative of Ukraine's nuclear energy company Energoatom told Reuters.
with DPA
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