The separatists countered with their own march – by parading captured Ukrainian troops through the streets of their main stronghold, Donetsk.
The counter marches come as intense shelling was heard around Donetsk this weekend.
Nearby, government forces exchanged gunfire with rebels in Ilovaisk, a small town where both sides are pitched in fierce street battles for territory.
Russian President Vladimir Putin meets his Ukrainian counterpart next week, in what diplomats say is the best chance for peace in months.
But Sunday’s rival events highlight the divide that needs to be bridged in those talks, if a compromise on Ukraine is going to be reached.