Knighthood for author was condemned by a number of Muslim countries and organisations.
Echoing Brown’s words, a foreign office spokesman said: “There is no excuse for such threats or acts of violence.
“[Britain] will not allow terrorists to undermine the British way of life.”
Rushdie, whose 1988 book The Satanic Verses was viewed as blaspheming Islam by some Muslims and led to an Iranian fatwa calling for his death, was made “Sir Salman” by Queen Elizabeth II in June.
Zawahiri said in his audio recording that Britain was hypocritical for giving Rushdie the knighthood under the banner of freedom of speech.