Piquet used a Brazilian Portuguese racial slur to describe seven-time champion Hamilton during a high-speed collision involving Hamilton and Max Verstappen at the Silverstone Grand Prix last year.
Verstappen is dating Piquet’s daughter, Kelly.
The racist term was used by the three-time F1 world champion in November last year but only recently came to light when the interview was published on Monday.
“I would like to clear up stories circulating in the media about a comment I made during an interview last year,” Piquet said in a statement sent to CNN.
“What I said was thoughtless, and I am not defending it, but I will clarify that the term used is one that has been widely and historically used colloquially in Brazilian Portuguese as a synonym for ‘guy’ or ‘person’.’ and was never intended to offend.
“I would never use the word I have been accused of in some translations. I strongly condemn any suggestion that the word was used by me for the purpose of demeaning a driver because of their skin color.
“I apologize wholeheartedly to everyone affected, including Lewis, who is an amazing driver, but the translation in some media now circulating on social media is not correct.
“Discrimination has no place in F1 or in society and I am happy to clarify my thinking in this regard.”
On Tuesday, Formula 1, Mercedes and the FIA condemned Piquet for using the racial slur and Hamilton responded to Piquet’s comments in a series of posts on Twitter, writing: “Vamos focar em mudar a mentalidade” – Portuguese for “Let’s focus on changing the mindset.”
Hamilton, who has the most race wins in F1 history, said “now is the time to act” against racism.
“It’s more than language. It’s archaic mentalities [that] have to change and have no place in our sport,” Hamilton said on Twitter. “I’ve been surrounded by these attitudes and targeted my whole life. There was a lot of time to learn. The time has come to act.”
Piquet’s comments were widely condemned in the sport.
Fellow Briton George Russell has come out in favor of his Mercedes team-mate.
“The fact that he and so many others STILL have to deal with this behavior is unacceptable. We all need to stand together against any form of discrimination.”
“Comments made to Lewis must not be tolerated, and we must continue to push for a more diverse and inclusive sport. We must eliminate discriminatory behavior and racist language in all its forms, not only in our sport, but also in our society.”
In a powerful post on his Instagram story, McLaren driver Daniel Ricciardo said: “Discrimination and racism have no place in this sport or in our society. Those who still choose to spread hate and use these words are not my friends.
“I want to thank Lewis and all the work he has done on and off the track to not only spread messages of equality, but to fight this hate.
“I’ve never dealt with racially motivated actions, but he has done it all his life. Yet every time his response to hate is driven by maturity, positivity and educating the world about the way we should act. I am with him and will do everything I can to follow and support.”