He said in a BBC radio interview that the fight against extremism "will have to be fought out not just militarily, but culturally and ideologically.
"I want to bring moderate and mainsteam opinion from all the different faiths on the side of saying: 'Look, we all stand together against this extremist violence.'
"And I want to bring the people in all the different countries of the world together to say that we will not tolerate an extremist threat that is being practiced in every continent of the world irrespective of events in one country or another."
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.