Nelson Piquet says his racially abusive remarks about Lewis Hamilton were "ill thought out".
The 69-year-old said he "strongly condemned any suggestion the word was used by me with the aim of belittling a driver because of his skin colour".
"I apologise wholeheartedly to anyone that was affected, including Lewis," three-time world champion Piquet said.
Hamilton responded on Tuesday by saying that "archaic mindsets need to change", adding: "It's more than language.
"I've been surrounded by these attitudes and targeted my whole life. There has been plenty of time to learn. Time has come for action."
Piquet said he "made no defence" of the remarks, but added that the term he used "is one that has widely and historically been 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."
He added: "The translation in some media that is now circulating on social media is not correct. Discrimination has no place in F1 or society and I am happy to clarify my thoughts in that respect."
Sources in F1 have said that Piquet, who won the 1981, 1983 and 1987 world titles, will not be allowed back into an F1 paddock following his comments.
He has long been a controversial character renowned for making provocative and insulting remarks about rivals.
Last year, he courted further controversy when he chauffeured Brazil's far-right President Jair Bolsonaro on the country's Independence Day.
And on Tuesday Brazilian novelist and lyricist Paulo Coelho condemned Piquet on social media.
"Dear Lewis Hamilton," Coelho wrote. "Piquet is currently the driver of the worst president in our history. His racist remarks shows the desperate need to return to the spotlight.
"I apologise in the name of the Brazilian people, who respect and love you."
The sport has rallied for Hamilton since Piquet's remarks, which were condemned by F1, governing body the FIA and Hamilton's Mercedes team, while rivals Ferrari and McLaren also offered their support.
Red Bull, whose driver Max Verstappen is the partner of Piquet's daughter Kelly Piquet, have not commented.
On Tuesday a number of drivers also came to Hamilton's support.
Ferrari's Charles Leclerc wrote: "Knowing Lewis since I arrived in F1, he has always been extremely respectful to me and everyone that he meets.
"Those values should be the standard towards anybody around the world.
"The comments made towards Lewis should not be tolerated. We should continue to push for a more diverse and inclusive sport.
"We need to remove discriminatory behaviour and racist language in any form, from not just our sport, but our society as well."
Hamilton's team-mate George Russell, a director of the Grand Prix Drivers' Association, said: "Huge respect to LH. He has done more for the sport than any driver in history, not just on track but off it.
"The fact that he and so many others are still having to deal with this behaviour is unacceptable. We all need to stand together against discrimination of any kind."