"He's off the ventilator, so the road to recovery has begun," his agent, Andrew Wylie, wrote in an email to Reuters.
Rushdie was flown by helicopter to a hospital in Erie, Pennsylvania, for treatment after the attack.
Authorities in Iran have made no public comment about the attack, although hardline state media outlets have celebrated it with headlines including "Satan has been blinded" and some Iranians voiced support online for the stabbing.
Rushdie was stabbed 10 times, prosecutors said during Matar's arraignment, according to the New York Times.
A Hezbollah official told Reuters on Saturday that the group had no additional information on the attack on Rushdie.