Kabuga 84, was arrested in France earlier in May after 26 years on the run over suspicion that he had funded Rwanda's 1994 genocide of the Tutsis and moderate Hutus.
The genocide led to the death of an estimated one million people between April and July 1994.
The tycoon was arrested by French gendarmes on 16 May 2020, at 6:30am., in an apartment in Asnières-sur-Seine, a suburb of Paris where he resided under a false identity.
“We wish the suspect should be extradited home knowing that Rwanda will accord him a fair trial," Jean Pierre Dusingizemungu, President of Genocide survivors' Umbrella said.
Most genocide suspects are said to be on the run in African countries and other parts of the world.
Prior to the genocide, Kabuga was a well-known successful businessman within Rwanda.
Under the regime of former President Juvénal Habyarimana, which ran from 1973 to 1994, the Rwandan tycoon held significant political influence.
In 1997, the International Criminal Tribunal for Rwanda – an international court established by the UN in 1994 to judge people responsible for the genocide – indicted Kabuga for his role.
The tribunal, which was located in Arusha, Tanzania, was dissolved in 2015.
Its work was taken over by the United Nations International Residual Mechanism for Criminal Tribunals.
It was set up to perform the remaining functions of both the Rwanda tribunal and the International Criminal Tribunal for the former Yugoslavia.
Earlier this week, the Rwandan tycoon appeared before a French court which is expected to make the decision on whether to hand him over to the tribunal, which is based in The Hague, Netherlands and Arusha.
The defendant has asked to be tried in a French court.