"According to initial reports, the (casualties) are civilians," the rebels' news agency said, citing their "defence ministry".
Earlier, the ministry was cited by Russian news agency Interfax as saying it was actually a rebel fighter who died.
It was unclear what weapons had been fired, with the rebels first claiming Ukrainian forces had used tank fire, and then saying there were mortar rounds.
The Ukrainian army condemned what it described as a "provocation aimed at destabilising the situation in the east," spokesman Vladislav Seleznev told AFP.
The Organisation for Security and Cooperation in Europe (OSCE), whose observers are deployed in eastern Ukraine, could not immediately comment on the incident.