"He's off the ventilator, so the road to recovery has begun," his agent, Andrew Wylie, wrote in an email to Reuters.
"It will be long; the injuries are severe, but his condition is headed in the right direction."
Rushdie, 75, was set to deliver a lecture on Friday at the Chautauqua Institution in western New York state on the importance of the United States as a haven for targeted artists when a 24-year-old man rushed the stage and stabbed him.
The Indian-born writer has lived with a bounty on his head following the publication of his 1988 novel The Satanic Verses, which is viewed by some Muslims as containing blasphemous passages. In 1989 Iran's supreme leader Ayatollah Ruhollah Khomeini issued a fatwa, or edict, calling for his assassination.
The Iranian government said in 1998 it would no longer back the fatwa. But in 2019, Twitter suspended Iran's Supreme Leader Ayatollah Ali Khamenei's account over a tweet that said the fatwa against Rushdie was "solid and irrevocable".
Writers and politicians around the world have condemned the attack. US Secretary of State Antony Blinken on Sunday said Iranian state institutions had incited violence against Rushdie for generations, and state-affiliated media had gloated about the attempt on his life.
"This is despicable," Blinken said in a statement.
"The United States and partners will not waver in our determination to stand up to these threats, using every appropriate tool at our disposal."
In Iran's first official reaction to Friday's attack, the foreign ministry said no one had the right to level accusations against Tehran for the attack, for which Rushdie and his supporters were solely to blame.
Ministry spokesperson Nasser Kanaani said freedom of speech did not justify Rushdie's insults against religion.
"During the attack on Salman Rushdie, we do not consider anyone other than himself and his supporters worthy of reproach, reproach and condemnation," Kanaani told reporters on Monday.
"No one has the right to accuse Iran in this regard."
The suspect in the stabbing, Hadi Matar of Fairview, New Jersey, pleaded not guilty to charges of attempted murder and assault at a court appearance on Saturday.
Neither local nor federal authorities have offered a possible motive.
An initial law enforcement review of Matar's social media accounts showed he was sympathetic to Shi'ite extremism and Iran's Islamic Revolutionary Guard Corps (IRGC), according to NBC New York. The IRGC is a powerful faction that Washington accuses of carrying out a global extremist campaign.
Matar was the son of a man from Yaroun in southern Lebanon, according to Ali Tehfe, the town's mayor. Matar's parents emigrated to the United States, where he was born and raised, the mayor said, adding he had no information on their political views.
The Iran-backed armed group Hezbollah holds significant sway in Yaroun, where posters of Khomeini and slain IRGC commander Qassem Soleimani, who was killed by a US drone strike in 2020, adorned walls at the weekend.
A Hezbollah official told Reuters on Saturday that the group had no additional information on the attack on Rushdie.
Rushdie was stabbed 10 times, prosecutors said during Matar's arraignment, according to the New York Times. He was flown by helicopter to a hospital in Erie, Pennsylvania, for treatment after the attack.
Following hours of surgery, he was put on a ventilator and was unable to speak as of Friday evening. Wylie had said he would likely lose an eye and had nerve damage in his arm and wounds to his liver.
One of Rushdie's sons on Sunday said his father remained in critical condition but was able to say a few words after getting off the ventilator.
"Though his life changing injuries are severe, his usual feisty and defiant sense of humour remains intact," Zafar Rushdie wrote on Twitter.
