"Sixty more people are still there (in Kiev) who were not included into the first list and we have moved them to the second stage of exchange", said Daria Morozova, Human Rights Ombudsman for the self-declared Donetsk People's Republic.
On Tuesday, Poroshenko met with the relatives of the hostages, saying: "Nothing is more important than to return our people home", according to a presidential statement.
The prisoners, some of whom have been held captive for more than a year, arrived at a Ukrainian government checkpoint with their belongings.
Separatist leaders and a Ukrainian government representative agreed on the prisoner exchange last week with the mediation by the head of the Russian Orthodox Church. Putin is godfather to Medvedchuk's daughter.
The exact number of prisoners exchanged is uncertain.
There are also about 10-15 people who came for the swap, but refused to return to the areas controlled by the militants in Luhansk and Donetsk regions. But a recent escalation in hostilities has quashed hopes of an imminent end to the conflict, which is now the longest in Europe since the second world war. On same day, 23 December, warring parties in east of that country agreed anor ceasefire for end of year, but two days later re were new recriminations mutual attacks.
The transfer of 237 prisoners from the Ukrainian government side and 73 from the rebel side was the largest since the conflict erupted in 2014 in Ukraine's two eastern-most regions, which border Russian Federation.
OSCE observers have been monitoring the situation in Ukraine since 2014. A number of similar ceasefires have failed to take hold since the start of the conflict.
On Saturday, the US State Department said it would provide lethal anti-tank weapons to Ukraine to help its forces fight Russian-backed separatists. The Obama administration had consistently refused to approve Kiev's requests for USA lethal weaponry because it said the move risked provoking a risky escalation in the conflict.