JOHANNESBURG — The South African police said on Thursday they had opened a murder investigation into the death of an exiled former spy chief from Rwanda and critic of President Paul Kagame, 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, was found at the upscale Michelangelo Towers hotel. He was "dead on the bed," a police statement said. "Preliminary investigations revealed that his neck was swollen. A towel with blood and a rope were found in the hotel room safe. There is a possibility that 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 opposition Rwanda National Congress accused Mr. Kagame's government of seeking to assassinate its foes. "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.

While the authorities in Rwanda had no immediate comment on the death of Mr. Karegeya, they had frequently accused him of plotting violent revolution, blaming exiled Rwandans in South Africa for a series of grenade attacks around the time of elections in 2010.

"There cannot be any change through election but through violent means," Mr. Karegeya said at the time.

In 2011, Mr. Nyamwasa, Mr. Karegeya and two other exiled dissidents were tried in Rwanda in absentia and sentenced to 20 years in prison for threatening state security.

"We encourage the authorities to really look into the matter so that we know exactly what happened," Reuters quoted Rwanda's ambassador to South Africa, Vincent Karega, as saying on Thursday.

According to The Associated Press, Theogene Rudasingwa, an official of the Rwanda National Congress, said Mr. Karegeya had gone to the Michelangelo Towers to meet a man presenting himself as a friend of the opposition, who was identified only as Apollo.

The rivalries in Rwanda date to the 1980s, when Rwandans fought alongside Ugandan rebels supporting President Yoweri Museveni, who, once in power, sponsored Mr. Kagame's own insurgency. As the military spymaster, Mr. Karegeya wielded significant influence for a decade before he fell out with Mr. Kagame, who took power in 1994. He was stripped of his rank and fled the country in 2006.