In a videotape, excerpts of which were aired by Aljazeera on Friday, Ayman al-Zawahiri was apparently referring to recent comments by Donald Rumsfeld, the US defence secretary, who on 22 December hinted that the US military will soon begin reducing its troop strength in Iraq below 138,000.
"I congratulate my nation and bless Islam's victory in Iraq," he said.
"Oh my Muslim brothers, I told you more than a year ago that the pullout of America's troops from Iraq would be a matter of time and Americans are now begging to leave and negotiate with the mujahidin.
"Bush, the liar, was forced to announce in November 2005 that he would withdraw his troops from Iraq.
"Since Bush is addicted to lying, he justified his withdrawal by saying that Iraqi forces have become well-trained. But he did not set a timetable for the pullout.
Al-Zawahiri asked: "If your forces with all its aircraft, missiles, tanks and fleets are moaning, bleeding and looking for an escape from Iraq, then will the hypocrites, conspirators, infidels [the Iraqi government] resist what the 'greatest power in the world' has failed to resist?
"The timetable of withdrawal was set a long time ago and you [Bush] have to confess that you have been defeated in Iraq as you have been defeated in Afghanistan and will be shortly defeated in Palestine if Allah's willing."
Al-Zawahiri went on to call on Muslim nations and charity and relief organisations, particularly Muslim ones, to offer aid to their brethren affected by the earthquake in Pakistan.
"I call you not to offer aid to the Pakistani government," he said. He described its administration as corrupt, saying its army leadership took bribes.
He described the members of the ruling party in Pakistan as "a gang of hypocrites".
"I call on Islamic people's charity organisations to come to Pakistan and supervise the relief and charity works offered for those hit by the earthquake.
The previous videotape from al-Zawahiri, aired by Aljazeera last October, also called on Muslims to aid victims of the earthquake in Pakistan which killed an estimated 78,000 people and left 3 million homeless.
He also denounced the recent parliamentary elections in Egypt.
"The election was an American game in which Islamic movements were allowed to run with a limited number of candidates. And if they win, they will be a minority in the parliament.
"America paved the way for the ruling party to practice all its crimes and get the votes that have been already prearranged."