In an audio recording posted on a website, Zawahiri said: "I say to [Britain's Queen] Elizabeth and [former British Prime Minister Tony] Blair that your message has reached us and we are in the process of preparing for you a precise response."
Rushdie was knighted by the queen in June, bringing condemnation from a number of Muslim countries and organisations.
The author is accused of blaspheming Islam in his novel "The Satanic Verses," which triggered an international furore when it was first published in 1988.
Rushdie was forced to go into hiding for a decade after then Iranian supreme leader Aytatollah Ruhollah Khomeini issued a 1989 death sentence over the book.
Khomeini's successor, Ayatollah Ali Khamenei, said in January 2005 he still believed the British novelist was an apostate whose killing would be authorised by Islam.
Following Rushdie's knighting, Iran said the death sentence still stands.
Mohammad Ali Hosseini, the Iranian foreign ministry spokesman, said: "The stance of the Islamic Republic of Iran with regard to this issue has not changed from what was put forward by the Imam Khomeini."