Channel 4 bosses have ordered a review of Big Brother following the racism row, but say that the current Celebrity edition of the show will remain on air.
Channel 4 has insisted it handled the situation responsibly
Chairman Luke Johnson said that the Channel 4 board expressed "profound regret" for any offence that may have been caused.
The board had spent several hours discussing the alleged racist bullying of Bollywood star Shilpa Shetty.
The broadcaster had been facing calls to axe the show completely.
Mr Johnson said the board believed that last week's events on Celebrity Big Brother had triggered an important debate.
"Clearly many people were worried and offended by what they saw. I want to reassure them that we take the views of our audience very seriously and profoundly regret any offence that may have been caused."
Mr Johnson said the board had commissioned a review of the "editorial and compliance processes" of Big Brother.
"The board will receive a full report and seek to identify any lessons that can be learned for the future," he said.
He added that Channel 4 expected to hear from the regulator Ofcom in the near future detailing the nature and number of complaints about Celebrity Big Brother.
"All board members of Channel 4 abhor racism. We are also committed to ensuring that the channel continues to fulfil its remit to explore important social issues," he said.
Trevor Phillips, chairman of the Commission for Equality and Human Rights, said it was "disappointing" the Channel 4 board had not acknowledged any error.
"What I had hoped was that the Channel 4 board would at least acknowledge that what we witnessed was racial bullying," he said.
He said he would be writing to Culture Secretary Tessa Jowell to ask her to consider whether she feels the Channel 4 board has fulfilled their responsibilities.
As the row over Big Brother entered its second week, Jade Goody - widely seen as the focus of antagonism to Shetty - was said to be receiving treatment for depression.
Goody said her comments were a big mistake
A statement by her agent John Noel said: "Jade is completely distraught and is receiving medical attention for shock and depression.
"She has publicly apologised to Shilpa and to the country on national television. Jade has had the courage to say sorry, to face her critics and to try to make amends."
He suggested that Goody, 25, was now a victim of bullying herself by certain sections of the media.
Goody, who was evicted on Friday, appeared on GMTV on Monday admitting her behaviour in the Celebrity Big Brother House had been "nasty and ugly".
Over the weekend Channel 4 was forced to deny that Goody had been coached on what to say in her post eviction interview.
Media watchdog Ofcom said it had received about 40,000 complaints about the programme. Viewing figures for Friday's late edition of Celebrity Big Brother averaged 7.8 million - peaking at 8.8 million towards the end of the programme, according to unofficial overnight ratings.
Saturday's and Sunday's instalments averaged 3.1 million and 3.4 million viewers respectively.
Following Goody's eviction bookmaker William Hill slashed the odds for Channel 4 axing the current Celebrity Big Brother series to 50-1.
It is offering 3-1 that no further series will be commissioned and 6-1 that there will be no more series of the non-celebrity version.
Shetty is now odds-on favourite to win the show, with William Hill cutting her price from 5-1 ten days ago to 8-11 now.