They include two former heads of the Secret Intelligence Service MI6 - Sir Richard Dearlove and Sir John Scarlett.
Former UK ambassador David Manning and UK special representative to Iraq Sir Jeremy Greenstock have given evidence in both public and private.
The Chilcot inquiry is examining the UK's involvement in the 2003 military action in Iraq and its aftermath.
When it was first announced by then-prime minister Gordon Brown in June 2009 he initially said it would be held behind closed doors for security reasons.
But later, after widespread criticism, he said some sessions should be in public and it was up to the chairman, Sir John Chilcot.
Sir John said at the time he felt it was "essential to hold as much of the proceedings of the inquiry as possible in public" - and most of the hearings have been in public.
But the inquiry confirmed on Thursday that it had heard from 35 witnesses in private. Among those known about are Mr Manning, Sir Jeremy and the man who ran the British operations during the conflict, General Sir John Reith.
A full transcript of Gen Sir John's evidence was later published with five words blanked out, which the inquiry said was on "national security" grounds.
Its chairman, Sir John Chilcott, said of the 35 witnesses: "These hearings have given the inquiry valuable evidence which could have not be heard in public session without damaging national security or international relations.
"They have supplemented the inquiry's understanding as it takes forward its public work."
Thirty five people have given evidence to the Iraq Inquiry behind closed doors, it has announced.