"We have come to a clear view that David Nicholson is the chief executive of the board, he is the person who we wish very strongly to lead a strong executive team on the board.
"He is the person whose command of the detail of the NHS, and his commitment and his passion to its future, we believe to be fundamental to the success of the board."
The chairman said his statement was a "statement of strength" and added: "We look, David, to you to provide us with the leadership as we take through an exceptionally challenging set of changes."
Robin Bastin, of the campaign group Cure the NHS, set up by families of those who lost loved-ones at Stafford, was one of those who walked out of the meeting.
Speaking afterwards, he said: "I'm disgusted."
"It's outrageous for him (Sir David) to say he needed to go on running this when he has been responsible for all that has happened.
"He was in charge of the strategic health authority when all this was going on."
Around a dozen people held placards displaying Sir David's photograph accompanied by the words "Resign", "The man with no shame" and "Too many deaths, no accountability".
Robert Francis QC, who chaired the public inquiry into the Mid Staffs scandal, attended the meeting of the commissioning board to tell them the NHS needed a culture of "openness, transparency and candour".
He said: "Openness about welcoming complaints and concerns, and explaining what you're doing about them.
"Transparency about how well everything is going. And that means a balanced approach of acknowledging difficulties and deficiencies as well as, quite properly, claiming the credit for things that are going right."
He added that there needed to be "rigorous rules" to ensure staff are honest about the service, "so that you are not being fooled by providers and they are telling you the truth, the whole truth and nothing but the truth, as we like to say in court".
"You, and commissioners in general, should acknowledge your own individual responsibilities for promoting the necessary culture change of individual and collective responsibility."
Sir David told the meeting that he and his colleagues needed tro "absorb the criticism".
Saying the "real enemy" was complacency, he said: "What you need to do is absorb the criticisms and understand it in a deep way and do something about it.
"We need to put the entire weight of the NHS, both the patients and the people working in it, to shift that culture in the right way."
He said he was "very passionate" about improving services to patients and "very ambitious" about the NHS.
But Julie Bailey, founder of Cure the NHS, said it was "deeply disturbing" that Sir David had been given the board's backing.