The bloodshed in the town of Krasnoarmeisk occurred hours after dozens of guardsmen shut down voting in a referendum on sovereignty for the region.
An Associated Press photographer who witnessed the shooting said two people were seen lying unmoving on the ground and insurgent leader Denis Pushilin was quoted by the ITAR-Tass news agency as saying there were an unspecified number of deaths.
Several hours earlier, guardsmen came to the town about 20 miles from the regional capital, Donetsk, and dispersed referendum voting that was taking place outside the town hall and they took control of the building. In the evening, more guardsmen arrived in a van and a scuffle broke out with people who were gathered around the building. Then the guardsmen fired shots.
Eastern Ukraine has been gripped by unrest for the past month as pro-Russia insurgents occupied police stations and government buildings. Ukrainian forces have mounted a limited offensive to try to drive them out.
Ukraine and the West have accused Russia of fomenting or even directing the unrest in the east, with the goal of destabilizing Ukraine or finding a pretext for invasion. Russia has rejected the accusations.
The Donetsk and Luhansk regions on Sunday conducted referendums on declaring the regions as so-called sovereign people's republics. Leaders of the vote, which is regarded as illegitimate by the central government and the West, say that sometime after the referendum, a decision will be made on whether to remain part of Ukraine, declare independence of seek annexation into Russia.
CBS News correspondent Clarissa Ward reports from eastern Ukraine that the voting did not come anywhere near international standards. Booths out in the open, people openly voting twice, and other irregularities raised serious questions about the legitimacy or the operation.
There had been only sporadic violence connected with Sunday's vote. Insurgents in the city of Slovyansk, which has seen some of the most violent clashes between pro-Russian militants and government forces in recent weeks, exchanged fire with Ukrainian troops on the outskirts of the city overnight. The Ukrainian Defense Ministry said an army soldier was wounded in a mortar shelling near Slovyansk TV tower.