Christian Cooper then began filming Amy Cooper as she told him she's "going to tell them there's an African American man threatening my life".
She then called the police and made a false report as her dog, being yanked on its collar by her, yelped.
But Christian Cooper said the woman who called the cops on him is now having her life threatened, which he said was "strange" and "inappropriate and abhorrent and should stop immediately".
The incident was shared on social media by his sister, and sparked outrage, making global headlines, as Amy Cooper was labelled "racist".
Amy Cooper has since been sacked from her job at investment company Franklin Templeton after being briefly placed on administrative leave. She also willingly surrendered her dog to an animal rescue shelter after she was accused of animal cruelty.
She has apologised for the incident, but claimed she is "not a racist". She also said she's received threats, and told CNN in a recent interview her "entire life is being destroyed right now".
READ MORE:
• The Conversation: How the language of disease produces hate and violence
• Coronavirus fears trigger anti-China racism around the world
• Covid-19 coronavirus: Racial abuse, top official's plea for calm; US becomes epicentre, New York may be quarantined
• Gary Abernathy: Trump is not a racist. His voters aren't either.
"I think her apology is sincere," Christian Cooper told CNN on Tuesday. "I'm not sure that in that apology she recognises that while she may not be or consider herself a racist, that particular act was definitely racist.
"And the fact that that was her recourse at that moment — granted, it was a stressful situation, a sudden situation — you know, maybe a moment of spectacularly poor judgment. But she went there and had this racist act that she did."
He also said he'd been told since the video went viral, people had been making threats to her.
"I am told there has been death threats and that is wholly inappropriate and abhorrent and should stop immediately," he said.
"I find it strange that people who were upset that … that she tried to bring death by cop down on my head, would then turn around and try to put death threats on her head.
"Where is the logic in that?" he said. "Where does that make any kind of sense?"
"I'm not a racist. I did not mean to harm that man in any way," Amy Cooper said in an initial apology over the incident. She said she meant no harm to the larger African-American community.
"I think I was just scared," she said in an interview with CNN.
"When you're alone in the Ramble, you don't know what's happening.
"It's not excusable, it's not defensible."