Fourteen civilians died after being shot on Bloody Sunday
Former BBC television journalist Peter Stewart attended the tribunal in Londonderry on Wednesday.
He said the commanding officer of the parachute regiment, Colonel Derek Wilford, had given General Robert Ford the information and said he was sorry but that General Robert Ford patted him on the shoulder and said well done.
The inquiry is investigating the circumstances surrounding the deaths of 13 civilians shot dead by British paratroopers during a civil rights march in Londonderry on 30 January 1972.
Another man died later from his injuries.
Mr Stewart said he overheard the conversation between General Robert Ford and Lieutenant Colonel Derek Wilford, commander of the Paratroopers.
Mr Stewart reported on the 1800 news that night that Army Paratroopers met a "fusillade of terrorists' fire" on entering Derry's Bogside.
But he admitted to the Saville Inquiry on Wednesday that those words were not accurate and "an unguarded statement".
He said he had had four conversations with General Ford, who was supposed to have been in Derry that day merely to observe events.
Lawyers for the 13 people killed that day insist that General Ford was a key figure in the tragedy.
After his final conversation with General Ford, he said, Colonel Wilford "came running up to give his situation report".
Mr Stewart told the inquiry: "He said to General Ford something like 'We have found two bodies sir, and neither of them had a weapon. I'm sorry'.
"General Ford said something like 'Well done, Derek,' and patted him on the shoulder."
Mr Stewart said later the threats were the result of one thing - his having reported the death toll as two or possibly three.
He said he had believed this was the case when he left the scene - when people in the city watching it were already aware that it was much higher.
"Therefore the anger and the threats made might have been the result of the misconceived notion that the BBC was trying to whitewash the Army's activities of that day.
"It might have been quite an understandable reaction between the broadcaster and what was known on the ground."
The Bloody Sunday inquiry was established in 1998, is chaired by Lord Saville of Newdigate and is expected to run for another two years.