The Arabic-language satellite station Al Jazeera reported that the video, posted on the internet, calls US President George W Bush a liar who "failed in his war against Al-Qaeda."
Pope Benedict XVI was branded an "imposter for his attitude to Islam and the Arab world."
It was a reference to the Pope's recent speech in Germany in which, critics say, the head of the Roman Catholic Church seemed to link Islam and violence.
Zawahiri also calls for a holy war in Sudan's Darfur region against the "crusaders... of the UN," according to Al-Jazeera.
The United States has been leading international efforts to force Sudan to accept the deployment of a 20,000-strong UN peacekeeping force to halt ethnic violence in its western Darfur region.
At least 200,000 people have died and some 2.5 million others have fled their homes because of the unrest which began in early 2003 when African rebels launched a revolt to gain more autonomy from the Arab-dominated Khartoum government.
Egyptian-born Zawahiri is regarded as the ideological powerhouse behind Al- Qaeda and carries a US$25 million bounty for information leading to his arrest or death.