More than 18,000 people complained to the BBC over the broadcast, which saw social affairs correspondent Fiona Lamdin repeat a racial slur allegedly used in a suspected racially-motivated attack in Bristol.
After the broadcaster initially defended the report, Mr Hall said in a statement that the BBC “now accepts that we should have taken a different approach at the time of broadcast and we are very sorry for that”.
The apology came after BBC Radio 1xtra presenter Sideman, real name David Whitely, announced he was quitting the corporation over the news report on social media.
He said the broadcast was an “error of judgment”, adding it “feels like a slap in the face to our community”.
Mr Hall said the report had caused “distress” to many, adding: “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.”
The BBC would be changing its guidance on offensive language in its output, he added.
The story ran on the BBC News Channel and local news programme Points West on July 29th, but the broadcaster stopped running the report which featured the offensive language later that day.
“It should be clear that the BBC’s intention was to highlight an alleged racist attack,” the outgoing director-general said.
“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.”
Welcome apology
June Sarpong, the BBC’s director of creative diversity, welcomed the decision to issue an apology, saying she is “glad” that [Mr] Hall has “personally intervened to unequivocally apologise”.
Channel 4 News presenter Krishnan Guru-Murthy praised Mr Hall for the move, adding: “But once again it has taken a direct intervention by the DG to overturn a mistake on race previously defended by the BBC’s editorial policy managers.”
Larry Madowo, a US correspondent for the BBC’s World Service, also commented on the move, saying that despite being black he had previously not been allowed to use the racist term in an article when quoting an African American.
“But a white person was allowed to say it on TV because it was ‘editorially justified’,” he said.
This is not the first time Mr Hall has made an intervention following a backlash over the BBC’s handling of discussions around race in its news output.
In September, he reversed a ruling by the corporation’s Executive Complaints Unit after it said BBC Breakfast host Naga Munchetty breached editorial guidelines when she condemned comments made by Donald Trump after he told female Democrats to “go back” to their own countries.
