A video of Justin Bieber making the comments while sat with friends was published on the Sun on Sunday website on June 1st.
It was originally filmed as part of his Never Say Never documentary in 2011.
The 20-year-old has released a statement saying: “I apologize for offending or hurting anyone with my childish and inexcusable mistake.”
The British newspaper claims people around Justin Bieber have known about the clip for some time and have spent money keeping it out of the public eye.
In the video, Justin Bieber asks: “Why are black people afraid of chainsaws?”
Justin Bieber then finished his joke by making the noise of the chainsaw and repeating the phrase “Run n*****” five times.
Someone who cannot be seen on camera says: “Don’t even say it. Don’t say it.”
A female voice then says: “You could say motorcycle too right?”
Earlier on Monday, Floyd Mayweather posted a picture of himself with Justin Bieber on his Instagram account along with a statement of support.
“Justin has been nothing but kind to me, my daughters and sons over the years,” he wrote.
“We all make mistakes when we are young, it’s part of growing up. I am proud of what he’s doing as a 20 year old musician and business man.”
The 37-year-old boxer has been friends with Justin Bieber for a few years.
A statement from Justin Bieber said: “As a kid, I didn’t understand the power of certain words and how they can hurt.
“I thought it was ok to repeat hurtful words and jokes, but didn’t realize at the time that it wasn’t funny and that in fact my actions were continuing the ignorance.
“Thanks to friends and family I learned from my mistakes and grew up and apologized for those wrongs.
“Now that these mistakes from the past have become public I need to apologize again to all those I have offended.
“I’m very sorry. I take my friendships with people of all cultures very seriously and I apologize for offending or hurting anyone with my childish and inexcusable mistake.
“I was a kid then and I am a man now who knows my responsibility to the world and to not make that mistake again.
“Ignorance has no place in our society and I hope the sharing of my faults can prevent others from making the same mistake in the future. I thought long and hard about what I wanted to say but telling the truth is always what’s right.
“Five years ago I made a reckless and immature mistake and I’m grateful to those close to me who helped me learn those lessons as a young man. Once again….I’m sorry.”
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