Stanislas Mbanenande, 54, an ethnic Hutu, is charged with genocide and crimes against international law and faces up to life in prison if convicted.
He allegedly took part in massacres between April 12 and June 30, 1994 that left thousands dead.
The indictment describes Mbanenande as having taken an "informal role as a lower-level leader among young Hutus who sympathised with, or came to sympathise with, Hutu extremism."
It also states that his leadership status was borne out by the fact that he possessed an automatic firearm, which he is said to have fired into crowds.
Mbanenande allegedly murdered or recruited young men to take part in massacres.
He was ordered to stand trial in Sweden after Stockholm was unable to comply with a request to extradite him to Rwanda, where he has been given a lifetime sentence in absentia, due to the fact that he obtained Swedish citizenship in 2008.
He has denied all charges following his arrest in December last year under an international arrest warrant.
Mbanenande has been in Sweden since 2007, when he joined his family and obtained a residency permit on family reunification grounds.
The April 6, 1994 killing of Rwanda's Hutu president Juvenal Habyarimana triggered a genocide in which 800,000 people, mostly from the Tutsi minority, were killed, according to UN figures.
The trial is expected to take several months and will move to Rwanda for a few weeks to hear witnesses.