The former Generation Game presenter, who is currently promoting a new play called Stand Up And Be Counted, also claimed that it is pointless apologising for a "perception" that people have of his comedy routines.
Speaking on Newsnight about his old stand-up gags as Chalky White, he said: "I always thought I wasn't a racist. I never thought I had to deny it because that was back in the 1970s and '80s when I did Chalky. Chalky ceased to exist 20 odd years ago and I would like to seriously apologise for any harm it did, but it would be like the Bay City Rollers apologising for making music that was acceptable in the 1970s.
"It is not something I would choose to do now and it's not something I have chosen to do for 20 odd years. But you can't just go around apologising for these people who have this perception of you."
He continued: "All these people were packing theatres - if the theatres were empty, I would have stopped. I would have made a financial decision, not a moral one. I was doing what I could do in the 1970s."
On the subject of racism, he said: "I think we've moved on now. I don't think racism exists like it did in the 1970s. For instance, I wouldn't do Chalky now because all my black friends don't have West Indian accents.
"I think racism and the talk that this play has stirred up is old hat. I don't see any racism at all really. We see the fear about Islam and the protesters, but that's only a lack of knowledge. I don't feel there is a great deal of racism and certainly not from me anymore."
Davidson, who described the BNP as "not very bright", added: "I think our country is a much better place for all the people in it. I've always picked out the little groups of people to have a laugh at, picking out the difference, and in my mind I wasn't hurting anybody. If I could go back and wipe that out, believe me I would, but it's what I do now that's important I think."