The U.S. military denied Monday that it had captured the most wanted militant in Iraq, Abu Musab al-Zarqawi (search).

Rumors of al-Zarqawi's capture were circulating just as the United States handed over sovereignty to an Iraq government, formally ending the U.S. occupation of Iraq two days ahead of schedule.

"This is not true, no matter how much I want to capture or kill Abu Musab al-Zarqawi on this special day, sadly we have not yet caught him," Brig. Gen. Mark Kimmitt (search), the deputy chief of operations, told Associated Press Television News.

Al-Zarqawi was rumored to have been picked up in Hillah, a predominantly Shiite city 60 miles south of Baghdad, the scene of a bloody car bombing Saturday night that killed about 20 people.

Al-Zarqawi, a Jordanian militant said to be connected to Al Qaeda (search), is suspected of masterminding a series of coordinated attacks on police and security forces last week that killed 100 people. He is also believed to be behind the beheading of two hostages, an American and a South Korean.

Meanwhile, a group claiming to represent fighters in the restive city of Fallujah threatened Monday to punish anyone working with U.S. forces who have clashed with Fallujah gunmen in recent days.

In a videotape obtained by APTN, the General Command of the Martyrs Groups of Fallujah repeated denials that they had any connection to al-Zarqawi.

The fighters, who appeared in the videotape wearing keffiyehs around their faces and carrying rocket-propelled grenades, said its fighters would "publicly punish everyone who deals and works with the Americans in hitting the resistance in Fallujah."

Coalition forces have maintained that al-Zarqawi has operated out of Fallujah, a hotbed of insurgent activity in the middle of the so-called Sunni Triangle. The U.S. military in the past week has struck three buildings in Fallujah that it claimed were al-Zarqawi safehouses.

But residents and clerics in Fallujah deny the claims, saying the United States has used al-Zarqawi as a pretext to target residents of the city who have stood up to the occupation of Iraq.