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.
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 an email, sent to all BBC staff, Lord Hall said: “I recognise that we have ended up creating distress amongst many people.”
His statement followed high-level discussions with BBC colleagues on Sunday morning.
The BBC’s director of creative diversity, June Sarpong, welcomed Lord Hall’s statement.
In a tweet, she wrote: “I am glad BBC director general has personally intervened to unequivocally apologise over BBC News’ use of the N-word.”
The Points West story described an attack on a 21-year-old NHS worker and musician known as K or K-Dogg, who was hit by a car on 22 July while walking to a bus stop from his workplace, Southmead Hospital in Bristol.
In his message, Lord Hall emphasised it was “the BBC’s intention was to highlight an alleged racist attack”.
“This is important journalism which the BBC should be reporting on and we will continue to do so,” he said.
“Yet despite these good intentions, I recognise that we have ended up creating distress amongst many people.
“The BBC now accepts that we should have taken a different approach at the time of broadcast and we are very sorry for that. We will now be strengthening our guidance on offensive language across our output.
“Every organisation should be able to acknowledge when it has made a mistake. We made one here.”
K-Dogg suffered serious injuries including a broken leg, nose and cheekbone in the attack.
Police said the incident is being treated as racially aggravated due to the racist language used by the occupants of the car.
In its initial defence, the BBC said that the organisation felt it needed “to explain, and report, not just the injuries but, given their alleged extreme nature, the words alleged to have been used”.
It said at the time that the decision, which was supported by K-Dogg’s family, had not been taken lightly and that the BBC understood people would be upset.
‘Error of judgement’
In addition to the 18,600 complaints made to the BBC over the news report, broadcast regulator Ofcom said it received 384 complaints. It makes the broadcast the second-most complained about since the BBC began using its current system in 2017.
In a video posted on Instagram on Saturday, DJ Sideman said the corporation had made “an error of judgement”.
“The BBC sanctioning the N-word being said on national television by a white person is something I can’t rock with,” he said.
“I just don’t feel comfortable being aligned with the organisation,” he added
The DJ’s actions received widespread support from colleagues and others in the entertainment industry.
Writing on Twitter, BBC Radio 1Xtra’s DJ Target said it was “a total shame” that it had taken the resignation of a “young black broadcaster” to trigger the BBC apology.
Labour’s Shadow Equalities Minister Marsha de Cordova said the BBC’s reasons for using the N-word were “obviously not good enough”.
Speaking ahead of Lord Hall’s statement, Ms de Cordova called on the broadcaster to apologise and “learn from this whole sorry episode”.
She was echoed by Labour MP Dawn Butler, who posted her support for Sideman on Twitter, saying the BBC should have apologised rather than “doubled down” on its justification.
BBC Radio London presenter Eddie Nestor described Sideman as a “king” following his resignation.
In a Facebook Live on Sunday he said the “way the story was reported” got in the way of the racial abuse suffered by the victim in the report.
In an Instagram post, BBC journalist Ashley John-Baptiste said he and other members of staff “just cannot fathom how it’s editorially justifiable for a white person to say the N-word”.
On Saturday, a spokesperson for 1Xtra called DJ Sideman “incredibly talented”, adding that the station was “disappointed” he had decided to resign.
“We absolutely wish him well for the future. The door is always open for future projects,” the spokesperson added.