Hadi Matar, of Fairview, New Jersey, pleaded not guilty to charges of attempted murder and assault in court on Sunday.
The alleged attacker “had been in direct contact with members of the Islamic Revolutionary Guard Corps on social media”, Vice magazine reported, citing “European and Middle Eastern intelligence officials”.
Iran has "categorically" denied its involvement in the attack.
In the first public statement by the government since the incident, Foreign Ministry spokesman Nasser Kanaani accused Mr Rushdie's supporters of being responsible.
“We, in the incident of the attack on Salman Rushdie in the US, do not consider that anyone deserves blame and accusations except him and his supporters." he said.
“Nobody has right to accuse Iran in this regard.”
Mr Matar is being held without bail, after prosecutors said he carried out a “targeted, unprovoked, pre-planned attack,” on Mr Rushdie.
Mr Matar's father has locked himself in at his home in Yaroun in southern Lebanon and is refusing to speak to anyone, the mayor of the town, Ali Tehfe, said on Sunday.
Mr Tehfe said Mr Matar's parents emigrated to the US and he was born and raised there, but his father returned to Lebanon several years ago.
“His father is in the country now but he has locked himself in and is not accepting to give any kind of statement to anyone. We tried with him, we sent people, we went and knocked the door but he is not agreeing to speak to anyone,” he told Reuters.
Mr Rushdie, author of The Satanic Verses, suffered serious injuries when he was stabbed in the neck and abdomen as he was about to give a lecture at the Chautauqua Institution, in western New York.
On Sunday, US Secretary of State Antony Blinken said Iranian state institutions had “incited violence” against the author “for generations”.
“State-affiliated media recently gloated about the attempt on his life. This is despicable,” Mr Blinken said.
Iran's government first commented on the situation on Monday when foreign ministry spokesman Nasser Kanaani said Mr Rushdie and his supporters were to blame for the attack.
Freedom of speech does not justify Mr Rushdie's insults upon religion in his writing, Mr Kanaani said.
Iran has no other information about Mr Rushdie's assailant apart from what has appeared in media, he added.
Iranian state-owned PressTV said “observers hinted at a potential link between the incident and a conspiracy to foment Islamophobia in the West”.
The Indian-born British-American writer has been recovering from his serious injuries since then.
On Sunday, Mr Rushdie’s son Zafar issued a statement about his father’s condition.
“My father remains in critical condition in hospital receiving extensive ongoing medical treatment. We are extremely relieved that yesterday he was taken off the ventilator and additional oxygen and he was able to say a few words,” he said.
Speaking to Vice, an unnamed Nato official said the attack “had all the hallmarks of a ‘guided’ attack”, where an intelligence service talks a supporter into action, without direct support or involvement in the attack itself.
Investigators have so far not revealed that there was a direct link between the Iranian government and Mr Rushdie’s attacker.
Another Middle Eastern intelligence official told Vice that it was unlikely the attacker decided to act on his own accord.
“A 24-year-old born in the United States does not come up with Salman Rushdie as a target on his own,” he said.
“Even an avid consumer of Iranian propaganda would have some difficulty finding references to Rushdie compared to all the other, modern enemies designated by the regime.”
$3 million offered to kill Rushdie
Iran’s former supreme leader Ayatollah Ruhollah Khomeini had issued a religious edict calling for Mr Rushdie’s death a year after The Satanic Verses came out in 1988.
A bounty of about $3 million was offered for anyone who killed Rushdie.
The book has been criticised by many Muslims for what they have described as a blasphemous interpretation of the Prophet Muhammad’s life, on which a character in the story is supposedly based.
Khomeini’s successor as supreme leader, Ayatollah Ali Khamenei, did not overturn or revise the edict and doubled down on its validity as recently as 2017.
“The decree is as Imam Khomeini issued,” he said.