Pro-Russian rebels shot down two Ukrainian fighter jets on Wednesday, not far from where a Malaysian airliner was brought down last week in eastern Ukraine, killing all 298 passengers on board.
A spokesman for Ukraine's military operations said the planes were downed near Savur Mogila, a burial mound in the Shaktersky region where a memorial marks ambushes by the Soviet army on occupying Nazis during World War II.
He said he did not have any information about the pilots.
Igor Strelkov, who is now in charge of the rebel ranks in the eastern city of Donetsk, said the separatists had brought down one plane and that the pilot had ejected. He gave no further details.
Fierce fighting raged near the rebels' two main centres in Donetsk and nearby Luhansk, where they have been pushed back by Ukrainian government forces, who have taken control of villages and suburbs around the cities.
Earlier on Tuesday, Kiev said the separatists were leaving their positions on the outskirts of Donetsk and retreating towards the city center.
Residents said the rebels, who rose up in April demanding independence from Kiev in the mainly Russian-speaking east, had dug trenches in downtown Donetsk outside the main university, where they have been living in student dormitories.
"In Donetsk, rebels abandoned their positions en masse and went towards the central part of the city," the headquarters of what Kiev calls its "anti-terrorist operation" said in a statement.
"It cannot be ruled out that the appearance of such movements could suggest the spread of panic and attempts to leave the place of warfare."
Residents said they had heard shelling during the night and a shell struck a chemical plant in the city, causing a fire.
Local health officials said 432 people had been killed and 1,015 wounded since hostilities started in the Donetsk region following the removal of a president in Kiev who was sympathetic to Moscow and after Russia's annexation of the Crimea region.