"You should worry about your presence in two areas - the first is the Gulf, from where you will be expelled, God willing, after your defeat in Iraq, and your economic ruin will be achieved," he said.
"The second is Israel, because the jihadi reinforcements are getting closer, with God's help and power, and your defeat there will put an end to the superiority of the Zionists and Crusaders."
The videotape, aired by Aljazeera, is the latest in a series of messages from Egypt-born al-Zawahiri, and comes as the US is commemorating the fifth anniversary of the September 11 2001 attacks in New York, Washington and Pennsylvania.
Osama Bin Laden and the al-Qaeda network have recently taken credit for the attacks, in which almost 3,000 people died.
Al-Zawahiri also described the situation in Afghanistan, where attacks on coalition forces by remnants of the Taliban regime which sheltered Osama Bin Laden and the al-Qaeda network have increased sharply in recent months, as "very good".
He said that US forces would be "pushed away" from the country by next summer, along with British, Canadian, and other Nato forces currently stationed in the country.
"Israel has been able to dominate Lebanon and Gaza only because Egypt has been totally removed from the conflict with Israel"
deputy head of al-Qaeda
The tape also showed Zawahiri condemning the Egyptian, Jordanian and Saudi Arabian governments for permitting the killing of Muslims in the Middle East, particuarly during the Israeli-Lebanon conflict.
"Israel has been able to dominate Lebanon and Gaza only because Egypt has been totally removed from the conflict with Israel," he said.
Zawahiri condemned United Nations resolution 1701, which brokered a ceasefire in the conflict, as it recognised Israel.
"The biggest problem with resolution 1701 and similiar resolutions designed to humiliate Muslims is ... its declaration of the existence of the Jewish state," al-Zawahiri said.
Al-Zawahiri's tape emerged a day after the As-Sahab website, al-Qaeda's media arm, posted a video of bin Laden and other commanders in a mountain camp, apparently planning the September 11 attacks.