Rio de Janeiro police investigator Giniton Lages told The Associated Press that blood spots believed to be those of the ambassador were found on a sofa inside the home of the wife.
According to reports, Amiridis had been spending the Christmas holidays with the Brazilian Oliveira and her family in family home in Nova Iguacu.
Amiridis had just taken the post of ambassador this year.
Oliveira denied participating in the murder itself, but confessed she knew of the crime.
The Greek foreign ministry confirmed on Thursday that Greece's Ambassador to Brazil, Kyriakos Amiridis, has been missing since Monday.
Mr Amiridis centre had been missing since Monday
Moreira told police he was romantically involved with 40-year-old Mrs Amiridis and that they planned the killing together.
Brazilian TV channel Globo showed images of a burned-out white auto in the Nova Iguaçu neighbourhood and reported that the licence plates matched those of Mr Amiridis' rental vehicle. Police suspect he was murdered.
An official at the Greek Embassy in Brasilia would not confirm the ambassador was missing, saying only that he was on vacation in Rio and expected to return to Brasilia on January 9. The pair have a 10-year-old daughter.
Brazilian President Michel Temer, in a letter addressed to Greek Prime Minister Alexis Tsipras, said the ambassador's killing had caused him profound sadness and he extended his condolences to the ambassador's family, friends and the Greek people. "It was a crime of passion", Magalhaes said, as quoted by Reuters. The host city of the 2016 Olympics has seen crime rates soar in recent months, fuelled by drug gang violence.
Brazil, especially Rio de Janeiro, has always been plagued by high rates of violent crime.
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P4 means primary four, which would have made Kaylee about 8 years old when she first enrolled in the school. Kaylee Rodgers has attention deficit hyperactivity disorder (ADHD) in addition to being autistic.