The Rwanda Defence Forces (RDF) said in a statement the Congolese soldiers crossed at Rubavu town, with one shot dead when he fired at a patrol and the other two arrested.
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 in a statement that three soldiers were on patrol along the common border when they inadvertently crossed into Rwandan territory.
"The Armed Forces of the Democratic Republic of Congo deplore the shooting of one of these soldiers," he said in a statement, adding that the army had made a request to repatriate all three of them.
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.
(Reporting by Philbert Girinema, Sonia Rolley and Yassin Kombi; Writing by Elias Biryabarema and Anait Miridzhanian; Editing by Andrew Cawthorne and Jonathan Oatis)
