The exchange was agreed between the two sides at talks in Istanbul last week and an initial swap of prisoners under the age of 25 was conducted on Monday.
The defence ministry in Moscow said the Russian soldiers freed in the latest handover were currently in Belarus, which borders both the warring countries, and would be returned to Russia for medical treatment and rehabilitation.
The group of Ukrainian prisoners consisted of seriously ill and severely injured soldiers, Ukrainian President Volodymyr Zelenskiy wrote on social media.
They will all receive immediate medical assistance, he said.
Among them were members of the army, the National Guard, transport services and border guards, Zelenskiy said.
Earlier, the Kremlin said it had been ready for several days to start handing over the bodies of Ukrainian soldiers killed in the war but that Ukraine was still discussing the details.
The planned transfer of thousands of war dead was the other tangible result of the Istanbul talks, which resumed last month after a gap of more than three years but have made no progress towards a ceasefire.
Russia has said it is ready to hand over the bodies of more than 6000 Ukrainian soldiers and receive any bodies of Russian soldiers which Ukraine is able to return.
But Kremlin aide Vladimir Medinsky said on Saturday that the Russian side had shown up at the agreed exchange point with the bodies of 1212 Ukrainian dead soldiers only to find nobody from Ukraine to take them.
Ukrainian President Volodymyr Zelenskiy has accused Russia of "trying to play some kind of dirty political and information game" around the issue of the exchanges.
Kremlin spokesman Dmitry Peskov said on Tuesday: "There is no final understanding. Contact is being made, numbers are being compared. As soon as there is a final understanding, then we hope this exchange will take place."
Russian state media has broadcast images of long white refrigerated trucks, containing bodies sealed in individual white bags, parked up near the border.Â
Ukrainian officials said on Tuesday Russia launched one of its largest air strikes on Kyiv in the war and struck a maternity ward in the southern city of Odesa in attacks that killed at least three people.
The overnight strikes followed Russia's biggest drone assault of the war on Ukraine on Monday and were part of intensified bombardments in what Russia says is retaliation for attacks by Ukrainian forces on Russia.
with DPA
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