Rushdie, 75, was taken off the ventilator on Saturday and was able to speak after being stabbed onstage at a literary event in New York State on Friday.
His son, Zafar Rushdie, said on Sunday the family was “extremely relieved” that the bestselling author had been taken off ventilator and supplemental oxygen on Saturday and that he was able to say a few words.
“After Friday’s attack, my father is still in critical condition in hospital, receiving extensive medical treatment,” he said in a statement on Twitter.
“While his life-changing injuries are serious, his usual snappy and defiant sense of humor remains intact,” he said.
The family expressed their gratitude to members of the public who bravely jumped to Rushdie’s defense and provided first aid after he was stabbed multiple times at the Chautauqua Institution in western New York.
The family thanked the police and doctors for their care. They also expressed their gratitude for the “outpouring of love and support from all over the world.”
“We ask for patience and privacy as the family gathers at his bedside to support and help him through this time,” the statement said.
Earlier, Rushdie’s ex-wife and celebrated TV personality Lakshmi tweeted: “Relieved @SalmanRushdie is moving on after Friday’s nightmare. Worried and wordless, can finally exhale. Now hope for a speedy recovery.”
Rushdie and Chennai-born Lakshmi married in 2004 and divorced in 2007. Lakshmi, 51, is herself an author and host of the popular culinary TV show TopChef, and was Rushdie’s fourth wife.
The New York Times reported that Andrew Wylie, Rushdie’s agent, said, “The road to recovery has begun. It will be long; the injuries are serious, but his condition is improving.”
Rushdie, who faced Islamic death threats years after writing “The Satanic Verses,” was stabbed by a 24-year-old New Jersey resident identified as Hadi Matar, the American national of Lebanese descent, on stage on Friday while being introduced at a literary event of the Chautauqua Institution in Western New York.
Rushdie was put on a ventilator after being stabbed by Matar.
Earlier on Saturday, Matar pleaded not guilty to charges of attempted murder and assault during a short hearing in court, where he was denied bail.
Matar was charged with attempted murder and assault in stabbing Rushdie and pleaded not guilty. He appeared in court wearing a black and white striped jumpsuit and handcuffed.
Chautauqua County District Attorney Jason Schmidt provided details of Rushdie’s injuries in court on Saturday during Matar’s arraignment.
The author’s injuries include three stab wounds to the right side of the front of his neck, four stab wounds to his stomach, a stab wound to his right eye and chest, and a laceration to his right thigh, the attorney general said.
“This was a targeted, unprovoked, pre-planned attack on Mr. Rushdie,” Schmidt claimed.
Matar faces up to 32 years if convicted on both charges, Schmidt said.
Rushdie lived in hiding and under police protection for years after the late Iranian leader Ayatollah Ruhollah Khomeini issued a fatwa in 1989 calling for his death in retaliation for his book The Satanic Verses.
Rushdie, the author of 14 novels, was knighted in 2007 for his services to literature.