Rushdie, 75, suffered a damaged liver and nerves in an arm and an eye, and he was on a ventilator, his agent Andrew Wylie said Friday evening. Rushdie was likely to lose the injured eye.
Rushdie's apparent attacker, Hadi Matar, was due in court on Saturday to face attempted murder and assault charges. A message was left with his lawyer seeking comment.
Matar, 24, was charged after the attack at the Chautauqua Institution, a nonprofit education and retreat center where Rushdie was scheduled to speak.
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Authorities said Matar is from Fairview, New Jersey. He was born in the United States to Lebanese parents who moved from Yaroun, a border village in southern Lebanon, the mayor of the village, Ali Tehfe, told The Associated Press.
Rushdie's book "The Satanic Verses" brought death threats after publication in 1988. It was seen as wicked by many Muslims who saw a character as an affront to the Prophet Muhammad, among other objections. The book was banned in Iran where the late leader Grand Ayatollah Ruhollah Khomeini issued a 1989 fatwa, or edict, calling for Rushdie's death.
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Police said the motive for the Friday attack was unclear. Matar was born a decade after "The Satanic Verses" was first published. Investigators were working to determine whether the assailant acted alone.
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Iran's theocratic rule and its state-run media gave no rationale for the assault. In Tehran, some Iranians questioned by the AP supported the attack on an author they believe degraded the Islamic faith, while others worried it would further isolate their country.
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An AP reporter saw the attacker confront Rushdie on stage and stab or punch him 10 to 15 times as the author was being introduced. Dr. Martin Haskell, a physician who was among those who rushed to help, described Rushdie's wounds as "serious but recoverable."
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Event moderator Henry Reese, 73, a co-founder of an organization that offers residencies to writers facing persecution, was also attacked. Reese suffered a facial injury and was treated and released from a hospital, police said. He and Rushdie had planned to discuss the United States as a refuge for writers and other artists in exile.
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A state trooper and a county sheriff's deputy were assigned to Rushdie's lecture, and state police said the trooper made the arrest. But after the attack, some longtime visitors to the center questioned why there wasn't tighter security for the event, given the decades of threats against Rushdie and a bounty on his head offering more than $3 million to anyone who killed him.