Kyriakos Amiridis, 59, had been missing since December 26. The ambassador’s body was found in a burnt-out car on the outskirts of Rio de Janeiro on December 29.
According to police, the ambassador’s Brazilian wife, Francoise Amiridis, plotted the murder with her lover.
Officer Sergio Gomes Moreira Filho confessed to strangling Kyriakos Amiridis to death, police said.
Francoise Amiridis, 40, has been detained along with Sergio Moreira, 29, and his cousin, Eduardo Melo.
Eduardo Melo is said to have been paid about 80,000 reais ($25,000) to act as a lookout.
The three suspects have been interrogated and will be held in police custody for another 30 days.
Investigator Evaristo Pontes Magalhaes described the murder as “a tragic, cowardly act,” which police are treating as “a crime of passion”.
At a press conference, Evaristo Pontes Magalhes said: “Francoise initially denied the facts. She said she had nothing to do with that. We managed to make her see that she had no alternative and that there was no point in continuing to deny it.
“She fell into contradictions, burst into tears and began to say that the police officer [Sergio Moreira] had carried out her husband’s murder.”
The investigator said Sergio Moreira had a fight with the ambassador and ended up killing him when he went to confront the diplomat about claims of violence against his wife.
Sergio Moreira said he acted in self defense. But Brazilian police have dismissed his statement.
They say the police officer’s cousin, Eduardo Melo, confessed to moving the ambassador’s body and gave full details of the plot to murder Kyriakos Amiridis, implicating both Sergio Moreira and Francoise Amiridis.
Kyriakos Amiridis had traveled from Brasilia to the city of Nova Iguacu, north of Rio de Janeiro, to spend the Christmas and New Year holidays there with his wife and her parents.
The couple had been living together for 15 years and their daughter is 10 years old, local reports said.
Francoise Amiridis reported her husband missing on December 28.
She told police that Kyriakos Amiridis had left on December 26 in a car he had rented. The burnt-out vehicle was found on December 29 under a flyover on one of the main access roads to Rio with a body inside.
The body was burned beyond recognition, but police said it was that of Kyriakos Amiridis.
Investigators also said that they had found blood stains on the sofa in the house where the couple was staying and say he was probably stabbed to death there.
Kyriakos Amiridis served as consul in Rio de Janeiro between 2001 and 2004 and returned to Brazil as ambassador earlier this year.
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