JOHANNESBURG — The South African police said on Thursday that they had opened a murder investigation into the death of an exiled former spy chief from Rwanda, who was found dead in a hotel room with signs of possible strangulation.

The body of Patrick Karegeya, a onetime head of Rwanda’s military intelligence who was a critic of the Rwandan president, Paul Kagame, was found on Wednesday on a bed at the upscale Michelangelo Towers hotel, a police statement said. His neck was swollen and a bloody towel and rope were found in the hotel room safe, the statement added, saying he might have been strangled.

The killing raised the prospect of Rwanda’s political feuds spilling far beyond the country’s borders. Mr. Karegeya, 53, a former ally of Mr. Kagame who turned against him, fled to South Africa along with a former army chief, Faustin Kayumba Nyamwasa, several years ago after being accused of plotting a coup.

Mr. Nyamwasa survived a shooting in the driveway of his home here in 2010.

As on that occasion, the Rwanda National Congress, an opposition political organization, accused Mr. Kagame’s government of seeking to assassinate its enemies. “By killing its opponents, the criminal regime in Kigali seeks to intimidate and silence the Rwandan people into submission,” the group said in a statement on Thursday.