Monday's video was his first appearance since a US air strike that targeted him on 13 January in Pakistan.
Al-Zawahiri said he had survived the raid which he said killed "innocents".
The air strike hit a building in the eastern Pakistan village of Damadola, reportedly killing four al-Qaida leaders.
Thirteen villagers were also killed in the strike, angering many Pakistanis.
The video appeared to be recorded this month, as it mentioned a call for a truce issued by bin Laden in an audio tape Aljazeera said was recorded in January.
"US airplanes ... launched a raid on a village in near Peshawar after Eid al-Adha in which 18 Muslim men, women and children were killed in what they call the war against terror," al-Zawahiri said.
"They said this was intended to kill myself and four brothers but now the whole world has discovered their lies ...".
Egyptian-born Al-Zawahri and Saudi-born bin Laden are believed to be hiding in a mountainous area on the border between Pakistan and Afghanistan.
Pakistani intelligence sources said four top al-Qaida fighters were believed to have been killed in the 13 January raid which US officials say was aimed at al-Qaida number two.
Al-Zawahiri, shown wearing white robes and a white turban, said the US had ignored an offer from al-Qaida leader Osama bin Laden for a truce.
"Butcher of Washington, you are not only defeated and a
liar, but also a failure. You are a curse on your own nation," he said, referring to Bush. "Bush, do you know where I am? I am among the Muslim masses," he said.
"My second message is to the American people, who are drowning in illusions. I tell you that Bush and his gang are shedding your blood and wasting your money in frustrated adventures," he said, speaking in a forceful and angry voice.
The 13 January Damadola raid
was targeted at al-Zawahiri
Al-Zawahiri added: "The lion of Islam, Shaikh Osama bin Laden, may God protect him, offered you a decent exit from your dilemma. But your leaders, who are keen to accumulate wealth, insist on throwing you in battles and killing your souls in Iraq and Afghanistan and - God willing - on your own land."
The video came in the wake of a 19 January audiotape by bin
Laden in which he said al-Qaida was preparing attacks
in the US but he offered a truce "with fair conditions" to build Iraq and Afghanistan.
The tape was the first message from bin Laden in over a year.
Al-Zawahiri continued: "The American planes raided in compliance with Musharraf the traitor and his security apparatus, the slave of the Crusaders and the Jews.
Extent of savagery
"In seeking to kill my humble self and four of my brothers, the whole world has discovered the extent of America's lies and failures and the extent of its savagery in fighting Islam and Muslims," al-Zawahiri said.
Aljazeera said it was airing excerpts of the video, and it showed two short parts. It was not immediately known how long the entire tape was.
"You, American mother, if the Pentagon calls to tell you that your son is coming home in a coffin, then remember George Bush"
al-Qaida deputy leader
The al-Qaida number two vented fury at Bush and the US leadership, saying: "Your leaders responded to the initiative of shaikh Osama, may God protect him, by saying they don't negotiate with terrorists and that they are winning the war on terror. I tell them: You liars, greedy war mongers, who is pulling out from Iraq and Afghanistan? Us or you? Whose soldiers are committing suicide because of despair? Us or you?"
"You, American mother, if the Pentagon calls to tell you that your son is coming home in a coffin, then remember George Bush. And you, British wife, if the Defence Department calls you to say that your husband is returning crippled and burnt, remember Tony Blair."
Call to convert
Elsewhere in the tape - reported but not aired by Aljazeera - al-Zawahiri called on Bush to convert to Islam, telling him that if he did so he would "become a brother in the faith and God will forgive you your sins".
He warned Musharraf against co-operation with the Americans, threatening, "Your day of judgement is approaching".
Al-Zawahiri extended his condolences to Afghans and Pakistanis for those killed in the US raids, and called on Muslims in Afghanistan and Pakistan to support the Taliban leader Mulla Omar.