Departing BBC director general Greg Dyke says he was shocked by the findings of the Hutton Inquiry and does not accept all of the report.
Dyke says he does not accept all the Hutton report findings
He admitted mistakes were made in his response to the government's original complaints.
But he said Lord Hutton had "given the benefit of doubt to every government witness and not to any at the BBC".
Mark Byford, the acting director general, said the corporation recognised that it had made errors.
He said his duty was to bring "calmness, clarity, leadership" to the organisation.
"It has been a very, very difficult week - that's an under-statement," Mr Byford told BBC Radio 4's PM programme.
"I would say the BBC at the top ... has shown it recognises that it's been an extremely turbulent week.
"It recognises that it has lost - quite extraordinary for any organisation - both its chairman and chief executive, but ... it must move forward ... there have been mistakes, it's a learning organisation ... and will be stronger from it."
Mr Byford is leading an internal inquiry into what went wrong and the steps needed to ensure it does not happen again.
He said the BBC had "a duty of care" to all its employees, including the Today defence correspondent Andrew Gilligan whose report was at the centre of the David Kelly controversy.
He added: "There will be a due process to consider the implications of the staff involved. I will lead that process."
Earlier, Mr Dyke told BBC Radio 4's Today programme it was perfectly fair for people to "draw the conclusion that I don't accept all of the report".
"Our legal team were all very surprised by the nature of the report."
September 2002: Government produces dossier about alleged Iraqi weapons of mass destruction, including claim they could be deployed within 45 minutes
May 2003: BBC Today programme's Andrew Gilligan broadcasts report of claims Downing Street "sexed up" dossier, with 45 mins claim included against intelligence agencies' wishes
10 July 2003:Dr David Kelly named as suspected source of report as government continues to deny the story
17 July 2003: Dr Kelly found dead
August 2003: Lord Hutton begins six weeks of hearings about the circumstances around Dr Kelly's death
Mr Dyke suggested the implications for journalism coming from the report were a matter of grave concern for the media.
"Lord Hutton does seem to suggest that it is not enough for a broadcaster or a newspaper... to simply report what a whistleblower says because they are an authoritative source. You have to demonstrate that it is true. That would change the law in this country."
He said he had had to offer his resignation after the report but had not wanted to go.
Speaking outside his home in Twickenham, south west London, he said: "The governors were in an incredibly difficult position. Hutton was very critical of the BBC - so critical that the chairman had decided to resign and I too felt I had to resign.
"They decided I did not have their full support."
Ex-culture secretary Chris Smith said there had been no need for heads to roll at the BBC and called for next Wednesday's Commons debate on the Hutton report to examine the issues surrounding the Iraq war.
Tony Blair is under pressure to make a statement on the intelligence he presented to Parliament on Iraq's weapons after the US national security chief admitted for the first time there may have been flaws in the gathering of material about the Iraqi arsenal.
Downing Street says it will wait and see whether the Iraq Survey Group turns up evidence of weapons of mass destruction.
'Matter should rest'
The prime minister's official spokesman said Lord Hutton's report had been fair. "A dispassionate judge has looked at the facts and has made his judgment on
the facts. That's where the matter should rest.
"We accept there was a lot of emotion and a lot of anger yesterday but the
judge has reached his conclusions on his assessment of the facts and what people
should recognise is that this is the judge's verdict."
BBC director of news Richard Sambrook has sent an email to all staff saying he will be working with Mr Byford, senior editors and news managers to look at ways to rebuild trust in the corporation.
Meanwhile ministers have stressed the importance of a BBC independent of government influence in the wake of Lord Hutton's criticisms of the corporation.
Culture Secretary Tessa Jowell said: "A BBC that is nobody's lapdog, that challenges government and raises debate - that is in all our interests."