Woods, speaking to reporters while in Sydney to participate in the Australian Open, said he and Williams had spoken about the incident and that while he was "hurt" by it, the pair shook hands.
"Steve is certainly not a racist," Woods told reporters. "There's no doubt about that. It was a comment that shouldn't have been made. It was one that he wished he didn't make."
Williams, a native of New Zealand who was Woods' caddie for more than a decade, called his former boss a "black (expletive)" last week at a function in China.
"It was the wrong thing to say, something that we both acknowledge now and we're moving forward," Woods said. "He did apologize. It was hurtful certainly. But life goes forward."
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