"The transfer of fallen soldiers' bodies has begun in accordance with the Istanbul Agreements," Medinsky reported on his Telegram channel.
Russia has handed over 1,212 bodies of Ukrainian soldiers to Ukraine and received 27 fallen Russian soldiers.
"Now they can be laid to rest in a Christian manner. The work will continue throughout these days," he wrote.
On Thursday, Russia and Ukraine will begin urgent "sanitary exchanges" of heavily wounded prisoners from the front lines.