The man's voice on the tape, aired by Aljazeera on Friday, also said it was the "duty of every Muslim to liberate Palestine".
Al-Zawahri, a senior leader of al-Qaida, also called for attacking US interests. "In Palestine, we are not only facing the Jews but also the anti-Islam international alliance headed by the US crusaders.
"So, fighting Jews and leaving America without being attacked will not make the Americans or the crusaders lessen their aggression against us."
The speaker also urged Muslims "not to wait any longer, otherwise, we will be devoured, one country after the other".
On Friday night, an unnamed intelligence source told news agency AFP that US Central Intelligence Agency (CIA) analysts concluded the tape was authentic and the voice belonged to al-Zawahri.
Call to action
"The youth must not wait for anyone and must begin resisting from now and learn a lesson from Iraq and Afghanistan and Chechnya," al-Zawahri said.
In addition to the US and Britain, al-Zawahri mentioned Australia, France, Poland, South Korea and Japan, saying they had all participated in the occupation of Afghanistan, Iraq and Chechnya and gave Israel its "means of survival".
"It is the duty of every Muslim to liberate Palestine"
"O Muslim youths! This is our message to you. If we die or get captured, follow the path and do not betray Allah and the Prophet," al-Zawahri said.
The audiotape was the second to surface in less than a month.
On 9 September, Aljazeera broadcast a video of al-Zawahri proclaiming that the US would ultimately be defeated in Iraq and Afghanistan.
The CIA determined with a high degree of confidence that the tape was authentic. The US administration has offered up to $25 million for information leading to his killing or capture.