BBC News 24 said Gavyn Davies, chairman of the BBC board of governors, tendered his resignation after the publication of the Hutton report. He made no immediate comment.
"The BBC does accept that certain key allegations reported by Andrew Gilligan on the Today programme on May 29 last year were wrong and we apologise for them," BBC Director General Greg Dyke said.
Hutton's findings will strengthen BBC critics who say the broadcaster should fall under the oversight of media regulator Ofcom. Conservative leader Michael Howard said the case for outside regulation of the BBC "has never been stronger".
The broadcaster's feud with Prime Minister Tony Blair's government comes as the publicly funded broadcaster is about to undergo a parliamentary review of its charter, and at a time when the mandatory licence fee that provides most of its funding is under fire from the private sector.
Alastair Campbell, Tony Blair's former director of communications, who was at the centre of the dispute after being named by Gilligan as the official who "sexed up" the dossier, said the BBC would have to decide what action to take now.
"What the report shows very clearly is the prime minister told the truth, the government told the truth, I told the truth. The BBC, from the chairman and the director general on down, did not," Campbell told a news conference.
"The BBC will have to decide itself what action to take to restore its reputation and integrity."
The BBC made pre-emptive reforms ahead of the Hutton report's release on Wednesday. In December it appointed an executive to oversee complaints and compliance, and tightened rules about its journalists writing for outside publications.
The National Union of Journalists, representing Gilligan, said the BBC could face a strike if he was disciplined or fired. The union said the Hutton report was "selective, grossly one-sided and a serious threat to the future of investigative journalism".
"The obvious implication is that the BBC's governance structure will come under the spotlight," said Damian Tambini, a media law expert at Oxford University. "People are already starting to ask questions about whether such a powerful institution should govern itself."
- REUTERS
Gavyn Davies, BBC Chairman:
Resignation statement
Lord Hutton:
Report of the inquiry into the circumstances surrounding the death of Dr David Kelly
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