The state will target 30% of the population, starting from high-risked groups including people above 65 years and front-line health workers.
The foundation said on Friday that Rusesabagina “continues to suffer from medical maltreatment as he is detained in Kigali”.
The move could help boost Rwandan state revenues, hit by the effects of COVID-19, officials say.
The Catholic parish of Ruhengeri in the north of the country, where the priests are stationed, also risks closure.
After crossing the border with Burundi in Nyungwe Forest, the fighters were ambushed by RDF at 10 a.m. local time (0900 GMT), immediately arrested.
In court last month, Rusesabagina admitted his ties to the rebels but said the group was never meant to kill Rwandans.
But the tribunal in Tanzania’s northern town of Arusha faces both legal challenges and bureaucratic delays as it prepares for trial, experts told Reuters.
The NYT quoted Rwanda's spy chief as saying "he delivered himself here".