Ukrainian and Iranian authorities have said the recording between an Iranian pilot and air traffic controller is authentic.
The Ukrainian Army announced a pullback from the town of Zolote, in the region of Luhansk, had begun on Tuesday night, whilst Russian-backed separatists said they were also complying.
Former vice-president says Congress must hold the president accountable.
"This would be the most profound violation of the presidential oath of office certainly during this presidency," House Intelligence Chair Adam Schiff said.
Thousands took to the streets of Kiev on Sunday for the largest and most peaceful gay pride parade ever held in Ukraine, despite the presence of hostile protesters.
Vladimir Putin said he saw "nothing wrong" with easing the path to Russian citizenship for residents of separatist-controlled eastern Ukraine after the European Union condemned the move.
Ukrainians are voting in a presidential election with a choice between a TV comedian or a billionaire businessman