A separatist representative overseeing the exchange in a remote location on the frontline between the warring sides said 139 Ukrainian troops and 52 rebels were transferred.
Ukrainian President Petro Poroshenko wrote on his Twitter account that he was informed the process had begun by the national security service.
"In the near time, 140 of our heroes will be free," he wrote, without specifying further. His spokesman, Svyatoslav Tsegolko, later confirmed only 139 Ukrainian soldiers were released today and that another would follow in the coming days.
Elsewhere today, Ukraine's military and the Russia-backed separatist rebels accused each other of continuing to mount attacks a week after a cease-fire was called.
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Ukrainian security spokesman Col Andriy Lysenko said that one serviceman was killed and 40 wounded in attacks over the past day. He did not state a total number of attacks, but said there were 10 mortar attacks on Ukrainian forces in the village of Shyrokyne on the fringes of the strategic port city of Mariupol.
The rebels claimed Ukrainian forces launched 15 shelling attacks overnight, including on parts of Donetsk, the largest rebel-controlled city.
An agreement reached by the leaders of Ukraine, Russia, Germany and France called for the guns to go quiet tomorrow.
The warring sides were supposed to begin drawing back heavy weapons from the front lines on Tuesday, but international monitors say they've seen no sign of that yet.
Heidi Tagliavini, an envoy for the Organisation for Security and Cooperation in Europe who led the talks with Russia and Ukraine that also included rebel figures, remained cautiously hopeful.
"There is not a single day in the Ukrainian conflict when we can feel sure what the next day will bring," she said.