In the video broadcast last night by the Al Jazeera satellite network, Ayman al-Zawahri said that Washington had rejected the offer of a truce from the al-Qa'ida leader and said that more attacks would be directed towards the US.
"Bush, you are not only defeated and a liar but, with God's help and might, a failure. You are a curse on your own nation and you have brought and will bring them only catastrophes and tragedies," he said, calling him a "butcher".
The recording is the first solid evidence that Zawahri survived a recent US air strike in Pakistan designed to kill him.
The strike in north-eastern Pakistan in the early hours of 13 January killed four other alleged al-Qa'ida members and at least 13 civilians, including children, but Zawahri was apparently not at the location of the missile strike.
The message also follows the release of an audio recording just five days after the missile strike by Bin Laden which offered a theoretical truce to the US people but also warned that there could be further attacks on US soil.
As with the Bin Laden recording, which the CIA said they believed was authentic, counter-terrorism officials in Washington last night told the Associated Press there was no reason to doubt the authenticity of this latest tape.
In the recording, Zawahri wears white robes and a white turban and stands against a black background. At one point he invites Mr Bush to convert to Islam and says his sins would then be forgiven.
He then taunts the President, saying: "Bush, do you know where I am? I am among the Muslim masses, enjoying God's blessing of their support, care, generosity and protection." The 13 January airstrike targetted a building in the Pakistani village of Damadola where it was believed Zawahri would be been attending an Islamic holiday dinner. US intelligence officials said later they believed Zawahri sent his aides in his place.
He also directed his speech to the families of British and US troops. "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," he said.Reuse content