The controversial presenter also begged his social media followers for forgiveness over the fact it appeared he did.
It followed reports about using the N-word while reciting a nursery rhyme though it was later edited out.
Clarkson said on Twitter he had made every effort to make sure he did not use the slur, but realised it might have sounded as though he had.
Clarkson said: "I was mortified by this, horrified. It is a word I loathe. Please be assured I did everything in my power to not use that word. And as I'm sitting here begging your forgiveness for the fact that obviously my efforts weren't quite good enough."
The BBC said Clarkson had explained the 'regrettable' incident and it had made "absolutely clear to him the standards the BBC expects on-air and off".