The fighting took place in Beni territory in North Kivu province from Saturday to Monday.
Army Spokesman, Jules Ngongo said the militiamen had tried to take the village of Kabasha.
They also ambushed UN peacekeepers, said Daniel Ruiz from the UN mission in Congo.
Two Nepalese and three Tanzanian peacekeepers were injured.
The army did not identify the militia group, but it identified itself as the National Movement for the Revolution.
The new movement wants to force President Joseph Kabila to organise elections by the end of the year, its spokesman, John Mangaiko, said.
Mangaiko accused the army of starting the fighting.
Kabila postponed elections due in November, in what his critics saw as an attempt to extend his rule beyond the constitutional two-term limit.
The move sparked widespread demonstrations in which dozens were killed.
The government and part of the opposition have agreed to stage the elections by the end of the year, but not everyone trusts the government to honour the pledge.
Dozens of armed groups vie for territory and mineral resources in eastern Congo.
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