In a portion of the same video, posted on the internet on Friday and released by the Virginia-based IntelCenter, al-Zawahiri addresses Bush: "Why don't you tell them how many million citizens of America and its allies you intend to kill in search of the imaginary victory and in breathless pursuit of the mirage towards which you are driving your people's sons in order to increase your profits?"
On Thursday, Islamist websites had said there would be a new video message posted by al-Zawahiri entitled Bush, the pope, Darfur and the Crusades.
In Friday's video, al-Zawahiri called Bush a "lying failure" for saying progress had been made in the war on terrorism.
"Bush you are a lying failure and a charlatan. It has been three and a half years [since the arrests] ... What happened to us? We have gained more strength and we are more insistent on martyrdom," he said.
Al-Zawahiri was referring to the arrest of al-Qaeda figures such as Khalid Shaikh Muhammad, the suspected mastermind of the September 11 attacks on the US.
"Bush, O failure and liar, why don't you be courageous for once and confront your people and tell them the truth about your losses in Iraq and Afghanistan."
Al-Zawahiri also called Pope Benedict a "charlatan" because of his remarks on Islam.
"This charlatan accused Islam of being incompatible with rationality while forgetting that his own Christianity is unacceptable to a sensible mind."
In a speech to a university in his native Germany on September 12, Pope Benedict quoted criticism of Islam and the Prophet Muhammad by 14th century Byzantine Emperor Manuel II Palaeologus, who wrote that everything Muhammad brought was evil and inhuman.
The pontiff said there was no room for violence in a religion based on reason.
Darfur 'holy war'
Al-Zawahiri also urged Muslims to engage in a holy war against proposed UN peacekeepers in Sudan's Darfur region.
"O Muslim nation, come to defend your lands from Crusaders masked as United Nations [troops]. Nothing will protect you except popular jihad [holy war]."
The European Commission said on Friday that Jose Manuel Barroso, its president, and a top EU aid official would go to Sudan this weekend to try to convince Khartoum to allow UN peacekeepers into Darfur.
Sudan has rebuffed a UN offer
to send peacekeepers to Darfur
The Sudanese government has repeatedly rebuffed a UN offer to send 22,000 UN peacekeepers to replace an ill-equipped and underfunded African Union force.
Sudan says the UN peacekeeping offer is motivated by Western colonial ambitions.
In a previous video posted on the internet to mark the fifth anniversary of the September 11, 2001, attacks on the US, al-Zawahiri said that the Gulf and Israel would be the next targets of al-Qaeda.
"You should worry about your presence two areas," he said in a message to Western powers. "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.
"And 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 Egyptian-born al-Zawahiri is regarded as the ideological powerhouse behind al-Qaeda and carries a $25 million US bounty for information leading to his arrest or death.