Ukraine and the rebels traded accusations over the hostilities that erupted yesterday.
The Ukrainian military also said six others were wounded, and claimed that 20 rebels were killed.
The rebels said two people were killed and two others were missing on their side and claimed that 10 Ukrainian soldiers died in the battle, according to Russian news agencies.
The spike in fighting in the Luhansk region is one of the worst in recent weeks.
Over 9,600 people have died in the fighting in eastern Ukraine since April 2014. A 2015 peace deal helped end large-scale fighting, but clashes have continued while progress towards a political settlement has stalled.