Two Congolese soldiers and a civilian were killed in a shoot-out on Tuesday in Bovata, near the town of Beni.
Isis also claimed to have established a province in central Africa, declaring it the “Central Africa Province” of the “caliphate” through its Amaq news agency.
It was not possible to verify the terror group’s claim, which included a higher toll of five soldiers killed and three wounded.
There are more than a dozen different militia groups and criminal outfits operating in this area of eastern DRC.
Witnesses at the scene blamed an Islamist group called the Allied Democratic Forces (ADF), which may have links to Isis, a UN source and local civil society leader told Reuters.
A report by New York University’s Congo Research Group and the Bridgeway Foundation published in November said the ADF had received money from a financier linked to Isis, suggesting ties between the Congo insurgents and other jihadis in Africa and beyond.
Congolese president Felix Tshisekedi has recently said Isis poses a threat to his nation and said his government would join the fight against extremists.
He has accused the ADF of allowing the infiltration of extremists.
Rival militia groups control parts of eastern Congo, which is rich in minerals, long after the official end of a 1998-2003 war in which millions of people were killed.
The town of Beni, near to where the attack happened, is suffering through both an Ebola epidemic and militia violence.
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