Mr Blinken said Iran’s state-affiliated media “gloated” about the "despicable" attempt on the author’s life.
He said Rushdie always stood up for “universal” rights of freedom of expression, of religion or belief, and of the press, and against “pernicious forces that seek to undermine these rights".
The US stands alongside the international community against those who would challenge these universal rights, Mr Blinken said.
Rushdie is on the road to recovery and showing signs of his "feisty and defiant" self, family and friends said on Sunday, days after a shocking stabbing attack left him on a ventilator.
Just hours after Friday's attack at a literary event in western New York state, the author underwent emergency surgery for potentially life-threatening injuries.
But his condition, while still serious, has since shown clear signs of improvement and Rushdie no longer requires assistance with breathing.
"He's off the ventilator, so the road to recovery has begun," his agent Andrew Wylie said.
"It will be long. The injuries are severe but his condition is headed in the right direction."
Salman Rushdie off ventilator and talking, agent says - video
The prize-winning writer, who spent years under police protection after Iranian leaders called for Mr Rushdie's killing over his portrayal of the Prophet Mohammed's life in his novel The Satanic Verses, was about to be interviewed when a man rushed on to the stage and stabbed him repeatedly in the neck and abdomen.
The suspect, Hadi Matar, 24, from New Jersey, was wrestled to the ground by staff and audience members before being taken into police custody.
Mr Matar was later arraigned in court and pleaded not guilty to charges of attempted murder. He is scheduled to appear again on August 19.
Rushdie's son said the family was "extremely relieved" that his father was breathing unaided and had been able to "say a few words".
"Though his life-changing injuries are severe, his usual feisty and defiant sense of humor remains intact," Zafar Rushdie said.
The event host, who was on stage with Rushdie and was also injured in the attack, said he initially thought it was a practical joke until he realised his famous guest was bleeding.
"It was very difficult to understand," Henry Reese, his face heavily bandaged, told CNN.
"It looked like a sort of bad prank and it didn't have any sense of reality. And then, when there was blood behind him, it became real."
Author Salman Rushdie stabbed in neck on stage - video
Police and prosecutors have provided scant information about Mr Matar's background or the possible motivation behind the attack.
His family appears to come from the village of Yaroun in southern Lebanon, although he was born in the US, according to a Lebanese official.
Rushdie, 75, had been living under an effective death sentence since 1989.
Iran's then-supreme leader, Ayatollah Ruhollah Khomeini, issued a religious decree, or fatwa, ordering Muslims to kill the writer for The Satanic Verses.
Rushdie, who was born in India in 1947, moved to New York two decades ago and became a US citizen in 2016.
Despite the continued threat to his life, he was increasingly seen in public, often without noticeable security.
Salman Rushdie attacked - in pictures
He recently told Germany's Stern magazine how his life had resumed a degree of normality after his relocation from Britain.
"Ever since I've been living in America … really, there hasn't been a problem in all that time," Rushdie said.
The stabbing led to international outrage from politicians, literary figures and ordinary people.
US President Joe Biden called it a "vicious" attack and praised Rushdie for "his refusal to be intimidated or silenced".
British leader Boris Johnson said he was "appalled".
Mr Matar is being held without bail and has been formally charged with second-degree attempted murder and assault with a weapon.