Washington accuses the 37-year-old Jordanian national of masterminding a series of devastating suicide bombings, including an attack against the UN compound in Baghdad and the assassination of Shi'ite cleric Ayatollah al-Hakim in al-Najaf -- an attack that killed more than 50 worshippers.
Al-Zarqawi also has claimed responsibility for the kidnapping and execution of several foreigners. Indeed, it is thought he carried out some of the beheadings himself.
But would his death make much of a difference to the situation in Iraq? Magnus Ranstorp, the director of the Center for the Study of Terrorism and Political Violence at the University of St. Andrews in Scotland, said he thinks killing al-Zarqawi might turn him into a martyr for many Iraqis. He argued it would be more effective to capture him alive.
"If they did capture [al-Zarqawi] and if there was a trial, I think it would be an important event to put him on trial, particularly for the attack on the United Nations, so I think it would be very important to capture him rather than to kill him, in order to, I think, win the war for influence, so to speak, and also to delegitimize some part of the insurgency," Ranstorp said.
Another unconfirmed report on a militant Islamist website suggested that the one-legged al-Zarqawi might have been shot through one of his lungs. The U.S. military, though, is resisting the temptation to celebrate. Its spokesman in Baghdad, Lieutenant Colonel Steven Boylan, said there is no way of knowing whether the report is fact or fiction.
The military's fear is that the message is a decoy intended to throw them off al-Zarqawi's trail. U.S. commanders in Iraq believe they are closing in, citing the arrest of more than 20 of his entourage. An Iraqi presidential adviser for security affairs, General Wafiq al Samarie, said on Al-Jazeera television yesterday that government troops had just arrested one of al-Zarqawi's closest aides.
Despite the appeal for prayers for al-Zarqawi in the website statement, sympathy appeared in short supply on the streets of Baghdad today. Some said he had caused too much suffering to innocent civilians.
"If he really exists, I want him to be dead as soon as possible because he has harmed the Iraqi people," said one man.
"The first thing we wish for al-Zarqawi for all the tragedies he has caused is for him to suffer more and more," said another. "We heard that he is wounded. He caused the deaths of many children and women and innocents. He has damaged our country, and God will punish him for what he has done."
Al-Zarqawi's network is seen as the main source of kidnappings, assassinations, and suicide bombings in Iraq and the driving force behind the recent spate of sectarian attacks on Shi'ites.
Washington is also increasingly convinced that al-Zarqawi is closely linked with Al-Qaeda -- despite reports of past differences with Osama bin Laden.
His prominence in the insurgency and his apparent ruthlessness make him the prime target for Iraq's fledgling security forces.