The Rwanda Defense Forces, RDF, said in a statement the Congolese soldiers crossed at Rubavu town.
One was shot dead when he fired at a patrol and the other two arrested, the statement added.
The soldiers had an AK-47 gun, four magazines with 105 rounds, a protective vest and sachets of cannabis, the RDF said.
Congolese military spokesperson Sylvain Ekenge said he was unaware of the incident.
Kinshasa has long accused Kigali of backing M23 rebels, led by members of the Tutsi ethnic group, in eastern Congo, who last year launched a fresh offensive in an area near Uganda, forcing more than 1 million people to flee.
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