Zawahri's comments were published on the Web site of the US-based SITE institute, www.siteinstitute.org, which searches and analyses militant networks. It said the video was broadcast on al- Qaeda's multimedia arm as-Sahab, which it monitors.

"Why send 20,000 only? Why not send 50 or 100,000? Aren't you aware that the dogs of Iraq are pining for your troops' dead bodies?" he said.

Bush plans to send a further 21,500 US soldiers to Iraq to help the government improve security, particularly in Baghdad.

It was al-Qaeda's first reaction to the US plan.

Zawahri taunted Bush further by inviting him to send the whole US army to Iraq, and said the "Mujahideen" were capable of destroying the equivalent of 10 armies.

He reiterated past offers to the US people of security by reaching an "understanding" with Muslims, and said peace would be impossible if Americans continued to follow the policies of Bush and his administration.

"If we are secure, you might be secure, and if we are safe, you might be safe," the Web site quoted Zawahri as saying.

Turning to Afghanistan, Zawahri said the United States had failed to deprive the Taliban of a haven there and had had to turn to Nato for help.

Zawahri urged Muslims to launch a jihad or holy war, saying Bush's plan to send more troops to Iraq made it an obligation for all Muslims to defend Islam.