The BBC has insisted it will not make any further comment about the source who alleged a dossier on Iraq had been embellished, or "sexed up", despite the offer of a deal by the defence secretary.
The BBC stands by Gilligan's reporting of his source
Geoff Hoon is to tell the corporation the name of the person the government thinks is the source for the report by BBC defence correspondent Andrew Gilligan.
A spokesman for Prime Minister Tony Blair said that all they wanted to know was whether they have got the right name.
The spokesman also corrected two errors made by the government on Tuesday.
He said that while it had claimed that the individual to be named by Mr Hoon was an MoD employee, the government now accepted he was paid by another department.
The government also accepted that the individual concerned had known Mr Gilligan for years rather than months as it had first claimed.
The latest twist in the row over the strength of the intelligence that led to the war in Iraq led the Conservatives and Liberal Democrats to renew their calls for a full judicial inquiry into the matter.
The Ministry of Defence (MoD) said on Tuesday that an official had come forward to say he had met BBC defence correspondent Andrew Gilligan a week before the broadcast of the story that has enraged Downing Street.
Chairman of the BBC board of governors, Gavyn Davies, responded to Mr Hoon in a letter saying that this was an "attempt to force" the BBC to break one of the fundamental principles of journalism.
"It is a cardinal principle of good journalism that sources should never be revealed, no matter how intense the pressure may be," he wrote.
"I am unable to accept your offer of confirming whether their name(s) match the person who has come forward at the Ministry of Defence."
Mr Hoon, who admitted he could not "specifically" say whether the official was Mr Gilligan's source, said he was disappointed by the BBC's decision.
"That is disappointing in this particular case because this particular source has been used by a journalist to impugn the integrity of the prime minister and indeed of the entire government.
"We are all, members of the public, entitled to know what is the basis for these allegations."
It is also not clear whether the MoD civil servant was the source for the story, with wide discrepancies in the accounts of the various protagonists.
The MoD released a statement saying the individual who had come forward was an expert on weapons of mass destruction (WMD), advised ministers and had known Mr Gilligan "for some months".
But the BBC said on Tuesday evening: "The description of the individual contained in the statement does not match Mr Gilligan's source in some important ways.
"Mr Gilligan's source does not work in the Ministry of Defence and he has known the source for a number of years, not months."
In its statement, the BBC said it stands "by Mr Gilligan's reporting of his source".
The BBC said Mr Gilligan "took comprehensive notes" during the meeting with his source, "which do not correspond with the account given in the MoD statement".
The corporation said Mr Gilligan's notes and account of what he was told by his source "are very similar" to notes of a conversation between Newsnight Science Editor Susan Watts and her source which led to the programme's reports on 2 and 4 June .
"These reports contained allegations consistent with the Gilligan report and she described her source as 'a senior official intimately involved with the process of pulling together the September dossier'".
Ms Watts and Mr Gilligan "have never met, spoken or corresponded" about these issues and the BBC does not know if the respective sources are the same ones because Ms Watts is unwilling to reveal her source.