BBC director general Tony Hall has apologised and said a mistake was made after a news report containing a racial slur was broadcast last month.
The N-word was used in full in a report about a racially aggravated attack in Bristol, broadcast by Points West and the BBC News Channel on 29 July.
The BBC initially defended the use of the slur after more than 18,600 complaints were made.
Lord Hall said he now accepts the BBC should have taken a different approach.
On Saturday, BBC Radio 1Xtra DJ Sideman – real name David Whitely – quit the station over the BBC’s use of the N-word.
He said “the action and the defence of the action feels like a slap in the face of our community”.
His actions were backed by a number of politicians and BBC staff, who offered support to the DJ.
In his statement, Lord Hall said: “I recognise that we have ended up creating distress amongst many people.”