Rugambage, acting editor for the Umuvugizi newspaper, was shot dead outside his home in Nyamirambo on Thursday (24 June).
Exiled editor of Umuvugizi, Jean Bosco Gasasira, has claimed Rwandan security officials are responsible for the murder.
He alleged that the attack was arranged after Rugambage published an article online linking Rwanda's chief spy to the shooting of General Kayumba Nyamwasa earlier in the month.
"I'm 100 percent sure it was the office of the national security services which shot him dead", he told VoiceofAmerica.com.
Rwanda National Police issued a statement saying they are "deeply concerned" by claims he was killed in a government attack, which they have dismissed as "fictional accounts being peddled by individuals and groups for political gains".
Police reports declare the crime was likely to have been one of revenge, linked to the 1994 Rwandan genocide.
Amnesty International immediately called for an independent commission of enquiry to be established.
Umuvugizi was suspended from publication earlier this year by Rwanda's Media High Council, which alleged the newspaper had broken media law.
It was forbidden to publish until after the August presidential elections, but moved online in May instead, with the General Nyamwasa shooting report going online on the same day as Rugamnage's murder.
Access to the site was later banned from within Rwanda.
On Friday (25 June), press freedom organisation Reporters Without Borders said the attack had appeared to be part of the government's attempts to control the election campaign process.
"As the August presidential election approaches, the government is organising a tightly controlled and monolithic electoral campaign in which all sources of criticism are being suppressed," they said. "This undertaking seems to have culminated in the ambushing and murder of this renowned journalist."
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