Al-Zawahri also congratulated Bush "on the success of his security plan" in Iraq and invited him to celebrate with "a glass of juice, but in the cafeteria of the Iraqi parliament in the middle of the Green Zone", referring to the site of a recent suicide bombing.
"We aren't waging jihad to lift oppression from the Muslims only, we are waging jihad to lift oppression from all of mankind"
The Site Institute said al-Zawahri also claimed al-Qaeda fighters in Iraq were getting "closer to victory over their enemy" despite continuing sectarian violence.
Al-Zawahri also spoke on a number of other topics in the video, including fighting in Afghanistan, Chechnya, Algeria, and Somalia.
He also referred to Saudi Arabia, the recent constitutional reforms in Egypt and the US Pentagon's release of the confessions of Khalid Sheikh Mohammed, who was captured in Pakistan in March 2003 and is said to be al-Qaeda's number three and who was allegedly behind the September 11 attack on the US World Trade Centre.
In it al-Zawahri called on minorities around the world to join the struggle against "oppression", saying: "We aren't waging jihad to lift oppression from the Muslims only, we are waging jihad to lift oppression from all of mankind, because Allah has ordered us never to accept oppression, whatever it may be."
The internet video is one hour seven minutes long, dated May and subtitled in English.