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Salman Rushdie (in September 2016)
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Brian Snyder / REUTERS
The writer reportedly spoke to investigators after the attack on Salman Rushdie.
The author was conscious in the hospital on Monday and answered questions from the officials, the TV station CNN reported, citing police circles.
However, it was initially unclear what the 75-year-old said exactly.
Requests to the police for confirmation of the information initially went unanswered.
The British-Indian author was attacked by a man at an event in western New York State on Friday.
Since then, Rushdie has been treated at a hospital for serious stab wounds.
On Sunday, his son Zafar Rushdie tweeted that he was doing better.
The condition of the 75-year-old is still serious.
But he was no longer connected to a ventilator and an additional oxygen supply.
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Assassination of Writer Salman Rushdie: Caught Up by an Ancient CurseBy Marc Pitzke, New York
After the crime, a 24-year-old was arrested and charged with attempted murder.
He pleaded not guilty in court.
There is no further information on a motive for the crime.
Years in hiding after death sentence in Iran
Rushdie has been persecuted by religious fanatics for decades because of his books.
The then Iranian revolutionary leader, Ayatollah Khomeini, had called for the author to be killed because of his work »The Satanic Verses« from 1988.
He accused Rushdie of insulting Islam, the Prophet and the Koran in his novel.
The death sentence was followed by Rushdie's dramatic escape and years of hiding.
He has lived in New York for more than 20 years.
US Secretary of State Antony Blinken said on Sunday that Iranian state media were "gleefully delighted" at the attack.
That was despicable, the statement said.
According to the Isna news agency, Iranian foreign ministry spokesman Nasser Kanaani said on Monday that there was no connection between Iran and the perpetrator.
With his work, Rushdie not only offended Iran, but also Muslims worldwide. "No one but him and his followers deserved guilt and accusations," Kanaani said.
His statements were Iran's first official statement since the attack.
hba/dpa