In an audio tape broadcast on Aljazeera TV on Friday, al-Zawahri said al-Qaida is pursuing Americans everywhere, but especially "in Afghanistan, in Iraq, in Palestine and in the Arab peninsula".
The tape, which has yet to be verified for authenticity, is said to have been made in November during the Muslim fasting month of Ramadan.
It marks the second anniversary of the battle of Tora Bora, when US-led forces in Afghanistan sought to wipe out al-Qaida chief Usama bin Laden and other leaders of the group.
"Two years after Tora Bora... we continue to pursue the Americans everywhere," the voice said. "The Americans have become weaker in Iraq. Their soldiers are cowards because they have no faith in their leaders.
"America has been defeated (by) our fighters despite all its military might, its weaponry."
And in an apparent reference to an attack on a Baghdad hotel in October, al-Zawahri said: "Americans have become unable to defend themselves and even to protect their biggest criminals and leaders such as (Deputy Defense Secretary Paul) Wolfowitz."
The Al-Qaida number two, who has repeatedly urged Americans to oppose the policies of President George Bush, told the American people: "How can we excuse you after all the warnings that we gave you. You reap what you sow."
"How can we excuse you after all the warnings that we gave you. You reap what you sow"
Ayman al-Zawahri to the American people
He also threatened Arab countries that provided "bases and help" to US forces to fight Muslims to be ready for "judgment day", saying the United States was getting ready to withdraw from the region.
Al-Zawahri, a former eye surgeon, was born in Egypt in 1951.
On the run
He was tried along with scores of Islamists for the 1981 assassination of President Anwar Sadat during a Cairo military parade.
In the 1990s, an Egyptian court sentenced him to death in absentia for activities linked to Jemaah Islamiya.
He is currently on the run from US forces who believe he is with bin Laden, probably somewhere along the Pakistan-Afghanistan border.
The United States leads a 12,000-strong force in Afghanistan after a 2001 invasion ousted the Taliban government which which gave shelter to al-Qaida.
The US blames the Islamist network for the September 11 attacks on the New York and Washington which killled around 3000 people.