"A message has been communicated to anyone who wants to speak out against the Kremlin: If you do, no matter who you are, where you are, we will find you, and we will silence you - in the most horrible way possible," Joyal said.
Vladimir Putin, the Russian president, and Russian officials have repeatedly denied involvement in the Litvinenko case.
Joyal and Litvinenko were acquaintances, said Oleg Kalugin, a former KGB counterintelligence chief who is now a US citizen and who met with Joyal several hours before he was shot.
Kalugin also said Joyal's condition was improving. Joyal works for National Strategies, a Washington-based government consulting firm.
The FBI was assisting in the investigation into Joyal's shooting.