The moderator of the event during which Sir Salman Rushdie was attacked onstage said his concern is for the writer “himself, but also what he means in the world”.
Henry Reese said the incident in New York highlighted more than ever the values that Sir Salman stands for.
The author, 75, suffered severe, life-changing injuries after being stabbed several times ahead of a lecture at the Chautauqua Institution, in New York, on Friday.
Asked how he was doing after the incident, Mr Reese told the BBC: “I’m doing well, everything is proceeding – I’m doing quite well.
“I think our concern is for Salman, and I mean that for himself, but also what he means in the world.
Asked what the incident meant for the importance of Sir Salman’s values, Mr Reese added: “There couldn’t be anything more vivid in its materialisation of our values.
“Our mission is to protect writers who are in sanctuary and to see Salman Rushdie assaulted for his life is unimaginably… it’s hard to describe what it is to see that happen in front of you.”
Mr Reese, who sustained severe bruising himself during the incident, said it would be “my ideal” to one day return to the venue and continue the conversation with Sir Salman.
“That would be my ideal to do that, and to see that happen and to not be in any way impeded in doing what we set out to do,” he said.
“To both show that these values will be defended and that they can be defended.”
Despite his “life-changing” injuries Sir Salman has retained his “usual feisty and defiant sense of humour”, his family has said.
The author suffered a damaged liver and severed nerves in an arm and an eye but was taken off a ventilator on Saturday.
It comes after Downing Street condemned the suggestion that Sir Salman might bear any responsibility for the attack as “ludicrous”.
The remarks came after an Iranian government official on Monday denied that Tehran was involved in the assault on the author, in remarks that were the country’s first public comments on the stabbing attack.
Nasser Kanaani, the spokesman of Iran’s Foreign Ministry, told journalists: “We, in the incident of the attack on Salman Rushdie in the US, do not consider that anyone deserves blame and accusations except him and his supporters.
“Nobody has the right to accuse Iran in this regard.”
He added: “We believe that the insults made and the support he received was an insult against followers of all religions.”
Sir Salman’s attacker, 24-year-old Hadi Matar, has pleaded not guilty through his lawyer to charges stemming from the assault and is due to appear in a US court on Friday.
The award-winning author has faced death threats over his book, The Satanic Verses, for more than 30 years.
Asked about the comments from Tehran, the Prime Minister’s official spokesman said: “Clearly it’s ludicrous to suggest that Salman Rushdie was in any way responsible for this abhorrent attack on him.
“This was not just an attack on him, it was an attack on the right to free speech and expression. And the UK Government stands both by him and his family but equally we will stand in defence of free speech around the world.”
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