The inquiry in London also learned on Thursday that Defence Secretary Geoff Hoon overrode the advice of his most senior civil servant to order Kelly to appear in public before a parliamentary committee set up to investigate the claims that London "sexed up" a dossier on Iraq.
Meanwhile, Kelly had told his bosses at the Ministry of Defence that he was "convinced" he was not the source for the contentious claims, broadcast by BBC radio journalist Andrew Gilligan in May, the inquiry also heard.
The claims that London "sexed up" a dossier on Iraq's weapons ahead of the US-led war in March and apparent suicide of Kelly has triggered a political crisis for British Prime Minister Tony Blair.
Blair, who is currently on holiday in Barbados, and Hoon are expected to be summoned to give evidence before the end of the inquiry which should last several weeks.
In a written reprimand sent to Kelly on July 9, the defence ministry's personnel director Richard Hatfield told the scientist he would not be punished for speaking to BBC journalist Andrew Gilligan ahead of his controversial radio report, but should seek explicit authorisation before any further contacts with journalists.
In the letter, published on Thursday by the inquiry into Kelly's death, Hatfield wrote: "I have concluded that although your behaviour fell well short of the standard that I would expect from a civil servant of your standing and experience, it would not be appropriate to initiate formal disciplinary proceedings."
"Your contact with Gilligan was particularly ill-judged. Your discussion with him in May has also had awkward consequences for both yourself and the department."
Letter from defence ministry to David Kelly
The letter added: "Your contact with Gilligan was particularly ill-judged. Your discussion with him in May has also had awkward consequences for both yourself and the department which could easily have been avoided."
The body of Kelly, a former UN arms inspector in Iraq and biological weapons expert, was found on July 18, three days after he was grilled by a parliamentary committee.
The independent judicial inquiry, ordered by Blair following Kelly's death, heard on Thursday that in a memorandum to Hoon, the defence ministry's permanent secretary Kevin Tebbit argued that allowing Kelly to go before the committee would attach "disproportionate importance" to his evidence.
"The man came forward voluntarily. He is not on trial," Tebbit's memorandum said.
But in a second memorandum, Hoon's office argued that it would be "presentationally" difficult to avoid putting Kelly before the committee and sent a further note to Foreign Secretary Jack Straw's office confirming that it had been decided that Kelly should give evidence.
BBC defence correspondent Gilligan said on May 29 that a senior British official, later confirmed by the BBC to be Kelly, had told him the government's September dossier on Iraq was "sexed up" against the wishes of the intelligence services.
Gilligan also used a newspaper article in June to report that Blair's key aide and media chief, Alastair Campbell, was responsible for inserting in the Iraq dossier the headline claim that Saddam Hussein could launch weapons of mass destruction within 45 minutes.
Alistair Campbell - accused of hyping the case for war
Kelly admitted in a June 30 letter that he had met Gilligan in a London hotel on May 22, the inquiry heard on Thursday.
But he insisted that the meeting had been to discuss Gilligan's experiences in Iraq during the recent war and "definitely not" to talk about the government's dossier.
The dossier had been mentioned only as a brief "aside" in the 45-minute conversation, Kelly said in his letter to Bryan Wells, director of the defence ministry's proliferation and arms control secretariat, within which he worked.
His recollection of the meeting differed so greatly from Gilligan's report on BBC radio's agenda-setting Today programme that it did not even occur to him for weeks afterwards that he might be the source, Kelly said in the letter.
He added in the letter: "I can only conclude one of three things: Gilligan has considerably embellished my meeting with him; he has met with other individuals who truly were intimately associated with the dossier; or he has assembled comments from both multiple direct and indirect sources for his articles."