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The row centres on a report by journalist Andrew Gilligan during the Today programme on BBC Radio 4 in which he said the government had "sexed up" its dossier on Iraq to boost public support for the war.
The BBC has until now refused to disclose the name of Mr Gilligan's source for the allegations.
But the director of news, Richard Sambrook, today said he could confirm that it was the senior Ministry of Defence adviser.
Mr Sambrook said the BBC believed it had correctly interpreted and reported the information obtained from Dr Kelly during interviews.
He added that the BBC had, until now, owed Dr Kelly a duty of confidentiality. He said he was "profoundly sorry" that his involvement as the source for the reports had ended in tragedy.
The body of Dr Kelly, a senior Ministry of Defence adviser, was discovered in woodland near his Oxfordshire home on Friday morning, with a knife and a packet of painkillers close by.
Police confirmed he had bled to death from a cut to his wrist.
Evidence to MPs
Before his death, Dr Kelly gave evidence to MPs that he had spoken to Mr Gilligan.
However, he said he did not believe he was the main source for the most controversial claims about the dossier.
He told MPs: "From the conversation I had I don't see how he could make the authoritative statement he was making from the comments I made."
The Prime Minister, Tony Blair, commented today, "I am pleased that the BBC has made this announcement.
"Whatever the differences, no one wanted this tragedy to happen."
The government has set up an independent judicial inquiry, chaired by Lord Hutton, to establish the facts surrounding Dr Kelly's death.
Both Mr Blair and the BBC have said they will cooperate fully.
At the Hutton inquiry into his death which began on 11 August, Dr Kelly's widow Janice said he had felt "totally let down and betrayed" by the Ministry of Defence.
Lord Hutton heard evidence from 74 witnesses over six weeks and viewed thousands of pages of evidence.
The report was published on 28 January 2004 and was highly critical of BBC governors for failing to investigate properly Downing Street's complaints.
As a result, the BBC chairman Gavyn Davies, the corporation's Director General Greg Dyke and journalist Andrew Gilligan resigned.
Lord Hutton absolved the government of any kind of "dishonourable, underhand or duplicitous strategy" in the leaking of Dr Kelly's name to the press.
But he said the Ministry of Defence was "at fault" for failing to tell Dr Kelly that his identity as the suspected source would be confirmed to journalists who suggested it.
He said Mr Gilligan's report that the Iraq dossier was sexed up was "unfounded" and that Joint Intelligence Committee chairman John Scarlett had acted to ensure the dossier was consistent with reliable intelligence.
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