The apology comes after a Points West broadcast which reported on an alleged racist attack in Bristol last week.
Within the broadcast, the reported referenced a racial slur which had been used by the attackers.
Today, Director-General Lord Tony Hall has issued an apology for the reference.
He said: “This morning I brought together a group of BBC colleagues to discuss our news coverage of the recent shocking attack on an NHS worker.
“I wanted us to look at the issues raised by the reporting and the strength of feeling surrounding it.
“We are proud of the BBC’s values of inclusion and respect, and have reflected long and hard on what people have had to say about the use of the n-word and all racist language both inside and outside the organisation.
“It should be clear that 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.
“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. It is important for us to listen – and also to learn. And that is what we will continue to do.”