The videotaped statement, broadcast by Aljazeera on Friday, was the first acknowledgment by al-Qaeda's central leadership of the death of al-Zarqawi, who was killed in a US air strike northeast of Baghdad on June 7.
The broadcast showed al-Zawahri, wearing a white robe and black turban, with a picture of a smiling al-Zarqawi over his left shoulder.
In the tape, al-Zawahiri said al-Zarqawi was "a soldier, a hero, an iman [Islamic cleric] and the prince of martyrs".
Al-Zawahiri addressed George Bush directly in the broadcast, and vowed to avenge al-Zarqawi's death.
"Yes O Bush, none of us is killed without us avenging him, with the help of God," said al-Zawahiri.
"You are not facing individuals but the whole of the Muslim nation.
"America will not dream in security until security has become a reality in Palestine and the other Muslim countries."
Among other things, Al-Zawahiri criticised Turkey for being a secular country which welcomed US bases and recognised Israel.
He also attacked Nuri al-Maliki, the Iraqi prime minister, and Zalmay Khalilzad, the US ambassador to Iraq, saying al-Maliki "trades with Islam" for power and describing Khalilzad as "the Afghan apostate".
Al-Zarqawi had pledged
allegiance to bin Laden
Al-Zawahiri did not mention the new leader of al-Qaida in Iraq, which the group has declared to be Abu Hamza al-Muhajer.
The omission of any reference to the successor might mean the tape was recorded before the successor was chosen, or it might indicate that al-Zawahiri does not endorse the new leader.
Dr Hussain Shaaban, an Iraqi writer and researcher, told Aljazeera that "al-Zarqawi's death has significantly affected al-Qaeda network in Iraq, so the videotape was meant to raise the morale of al-Qaeda members and their supporters in Iraq".
Speaking to Aljazeera from Cairo, Diya Rashwan, an expert in Islamic groups' affairs at al-Ahram Centre for the Political and Strategic Studies, said: "Al-Zawahiri has pointed to the alliance between al-Maliki and Khalilzad, which represents an alliance between the US government and the local government, in Iraq as much as in Afghanistan."
Mohamed Abu Ruman, a Jordan-based Islamic groups researcher, told Aljazeera: "Al-Zawahiri is aiming to raise the morale of al-Qaeda members and supporters whether in Iraq or elsewhere in the Arab world, in order to overcome the shock of al-Zarqawi's death.
"He wants to say that the death of any single al-Qaeda leader will not affect the message of al-Qaeda and the nature of its battle with the US.
"The picture [of al-Zarqawi] that appeared behind al-Zawahiri has a meaning. It gives an impression of the spiritual ties among al-Qaeda members."
For his part, a US security official said there was no reason to doubt the authenticity of the videotape, which he said was the eighth that al-Zawahiri had released since January 2006.
Speaking on condition of anonymity, he described al-Zawahiri's direct addresses to Bush as "jihadist bravado".
"It's part of their ongoing propaganda campaign to appear relevant by commenting on current topics," the official said.