"The American defeat in Iraq and Afghanistan has become just a question of time, God willing," he said in the tape telecast on Thursday.
"In the two countries, the Americans are between two fires: if they remain there they will bleed to death, and if they withdraw they will have lost everything."
The mujahidin are in a strong position in Afghanistan and have turned US plans in Iraq "head over heels", al-Zawahri said.
Pakistan is hunting for the right-
hand man to Usama bin Ladin
In Afghanistan, the mujahidin have driven US forces to "hide in their trenches", he said.
On the Darfur conflict, he said it was an example of US desire to split the Arab and Muslim world.
Al-Zawahri, the right-hand man of al-Qaida leader Usama bin Ladin, was seen wearing a white turban with a machine gun at his side in the videotape.
In the tape, shown two days before the third anniversary of the September 11 attacks on the US, he said: "East and south Afghanistan have become an open arena for the mujahidin. The enemy is limited to the capitals."
He added: "The Americans are hiding in their trenches and refuse to come out to face the mujahidin, as the mujahidin shell and fire on them, and cut roads off around them. Their defence is only to bomb by air, wasting US money as they kick up dust."
Al-Zawahri was last heard in March when Aljazeera aired a recorded message in which he called on Pakistanis to overthrow the US-allied Pervez Musharraf government.
"The Americans are hiding in their trenches and refuse to come out to face the mujahidin"
Al-Zawahri and bin Ladin last appeared in a videotape aired on Aljazeera in September 2003 in which the two were shown walking in a mountainous area together.
Pakistan, with US military back-up, has been trying to capture the two and other al-Qaida supporters thought to be in hiding in the mountainous region between Pakistan and Afghanistan.