"Allawi ... you have escaped many times, without knowing it, from well-organised ambushes that we laid," says the voice. "But we pledge to go all the way without giving up so that you will meet the same fate as Izz al-Din Salim."
Salim was the head of the now dissolved Iraqi Governing Council who was assassinated in a Baghdad car bombing on 17 May.
The purported recording by al-Zarqawi, who heads the Tauhid wa al-Jihad group, branded Iraqis who cooperate with the US-led occupying forces "the symbols of evil, infidel imams, the sign of betrayal", telling them: "You are hypocrites."
The 16-minute tape is entitled The Stance of Sharia (Islamic law) on the Government of the Iraqi Karzai - an allusion to the Afghan president, Hamid Karzai, installed after the US-led war that ousted the Taliban.
The recording also warns Iraqis against "what the Americans are preparing with the new Karzai of Iraq, to steal the victory from your children in Falluja", the Sunni town west of Baghdad.
It condemns the US military attacks on Falluja and, specifically, the air raids on Tuesday night.
The US military said it had struck a suspected safehouse used by al-Zarqawi in the town.
US forces attacked a suspected
al-Zarqawi safehouse in Falluja
"Wherever and whenever we find elements of the al-Zarqawi network, we will attack them," said chief spokesman Brigadier General Mark Kimmitt.
The tape denied that al-Zarqawi was in Falluja.
'Excuse for revenge'
The raids took place "on the pretext that I am in Falluja", the voice says. "It's wrong because these fools do not know that I move around Iraq, travelling up and down the country to be greeted as a guest by my brothers and my kindred."
"It's an excuse to take revenge" for the losses occupation forces have sustained in Iraq, the voice charges.
"Be on constant alert. Be watchful in the face of the enemy, finger on the trigger," it urges.
The United States has put a $10 million reward on his head.
The tape is posted at the web address www.qal3ah.org which forwards to www.hostinganime.com/iraqnews1/index.html.