Ukrainian forces also fought separatists in the neighbouring Luhansk region but there was no word about any casualties there.
The defence ministry confirmed that several people had been killed in the firefight near Donetsk but gave no precise death toll. It said the clash occurred when gunmen opened fire on an army checkpoint near the town of Volnovakha.
Separately, Ukrainian border guards said they had rebuffed an attempt by dozens of separatists, armed with grenade launchers and rifles, to enter the Luhansk region overnight from Russia. Several guards were hurt in the fighting.
Ukrainian security forces and the pro-Moscow separatists have clashed repeatedly in recent weeks in eastern Ukraine, where the breakdown of security has rattled the pro-Western interim government in Kiev.
Kiev has acknowledged that Sunday’s election cannot be held in parts of the Donetsk and Luhansk regions and has accused Moscow of deliberately seeking to undermine Ukrainian democracy, a charge echoed by the United States and European Union. Russia denies the legitimacy of the current Kiev government, which took over after mass street protests toppled Moscow-backed president Viktor Yanukovich in February.