Up to 500 insurgents attacked a convoy of government troops in a clash that lasted for several hours yesterday and killed 20 rebels outside the eastern village of Rubizhne, the ministry said.
It also said one soldier was killed early today near the same area after insurgents ambushed Ukrainian troops in a separate clash.
AP reporters saw three other bodies.
The claims from the Luhansk region, which has declared independence from Kiev, could not be independently confirmed. It was also not immediately clear why reports of such a major clash in a populated area took more than a day to surface.
Yet it was uncertain whether any voting could take place in eastern Ukraine, where, in addition to the fighting, a vote boycott and threats against election workers were disrupting the upcoming ballot.
AP journalists saw three dead from today's fighting in the eastern Donetsk region, another area that has declared independence. One rebel leader said 16 more people died today in fighting there, 10 soldiers, four rebels and two civilians, but there was no immediate way to verify his statement.