The human rights group said in a report members of a Rwandan military intelligence department, known as J2, had tortured civilians with electric shocks, beatings and sensory deprivation to force confessions.
J2 also held civilians in military detention without charge or trial for months on end, Amnesty said.
Rwanda’s Ministry of Justice said on Sunday that while some illegal detentions had taken place, these abuses were handled by the courts.
“These occurred as a result of over-exuberance on the part of individuals within the security services and were dealt with through the courts which immediately put in place corrective measures,” the statement said.
Rwanda did not directly address the allegations of torture detailed in Amnesty’s report, but the ministry said reports of torture are “investigated through established channels and are treated with the utmost seriousness”.
Last month a report by Human Rights Watch said Rwanda has been supporting a rebellion in neighbouring Congo, where the M23 rebels have committed widespread war crimes, including dozens of rapes and killings.
Rwanda has repeatedly denied involvement with M23 but many Western donors have suspended aid after a United Nations report concluded Rwandan officials were supplying the rebels with weapons and logistics.
Amnesty also called for donors to suspend funding for Rwanda’s security forces.
Between March 2010 and June 2012, Amnesty said it documented 45 cases of unlawful detention and 18 allegations of torture or ill-treatment at a military camp and in safe houses in Kigali.
Many men interviewed by Amnesty said they were rounded up after grenade attacks in Kigali in March 2010 and in the run-up to the presidential elections in August 2010, a poll which the incumbent president Paul Kagame won with 93 percent of the vote.
Many of those detained were later charged with threatening national security. Reuters