BAGHDAD Ñ Despite a fierce U.S. military offensive, the Mahdi Army has maintained control over at least one major Iraqi city.

U.S. officials said the Mahdi Army, loyal to Iranian-aligned Shi'ite cleric Moqtada Sadr, remains in control of Najaf. They said the Shi'ite militia still threatens significant parts of Baghdad and its suburbs.

The U.S. military and other coalition forces have launched Operation Resolute Sword in Shi'ite areas of central and southern Iraq in the offensive against Sadr. On Friday, the military was said to have captured the Shi'ite city of Kut, held by the Mahdi Army since Monday.

Officials said the most critical element of the U.S. military operation was in Baghdad, Middle East Newsline reported. They said U.S. air and ground forces have sought to foil Mahdi Army attacks against the U.S.-led Coalition Provisional Authority, military headquarters and key government installations in the Iraqi capital.

"In Baghdad, our forces remain on the offensive, conducting intelligence-based raids to destroy Sadr's militia as they attempt to intimidate the population," Lt. Gen. Ricardo Sanchez, head of the coalition forces in Iraq, said. "Despite attempts to incite violence, attack government facilities and disrupt the lives of Iraqis, coalition units are in firm control of Baghdad."

Officials said at least 2,000 Sadr combatants were battling U.S. and coalition forces in Baghdad. The Mahdi Army fighters entered Baghdad on April 4 as part of Sadr's campaign to launch a Shi'ite insurgency against the United States.

The United States has accused Iran of helping stir Shi'ite unrest in Iraq. But as late as Wednesday senior officials, including Defense Secretary Donald Rumsfeld, said there was no evidence of direct Iranian involvement in the current Shi'ite insurgency campaign.

For their part, Iranian government sources said the Iranian Revolutionary Guard Corps has trained up to 1,200 members of the Mahdi Army in bases along the Iraq-Iran border. On Friday, the London-based A-Sharq Al Awsat daily quoted sources in the IRGC's Jerusalem Brigade as saying that Iran established three military camps and training centers along the border with Iraq for the training of the Mahdi Army in both combat techniques and the production of weapons and explosives. The newspaper said the Iranian embassy in Baghdad recently distributed 400 cellular phones to Sadr combatants.

Sadr's militias, equipped with mortars, rocket-propelled grenades and light arms, continued to control portions of Kut and Najaf, officials said.

They said the U.S. military has been hampered by the presence of thousands of Shi'ite visitors for a religious pilgrimage that began on Friday.

"What is under control by Mahdi elements is the inner part of the city, [Najaf] the police stations and the government buildings," Sanchez said. "And we are very, very cognizant as a coalition of the religious observances that are ongoing right now and the holy shrine status and the special status of the city of Najaf."

Officials said the scale of Mahdi Army operations remained small, usually comprising a maximum of 20 combatants. In some cases, particularly in Baghdad, the Shi'ite force has used larger numbers but in what turned out to be poorly-coordinated attacks, officials said.

Still, Sanchez said, the United States will continue to target Sadr's militia and seek his arrest. He said the U.S. military, amid a major troop rotation, has not been plagued by manpower shortages. The military has 134,000 troops in Iraq and plans to introduce another 10,000 soldiers.

"Coalition military forces will conduct powerful, deliberate and very robust military operations until the job is done," Sanchez said. "We are taking advantage of these forces, and we will manage the redeployment to give us the combat power that is necessary to accomplish the mission at hand."

Officials said the U.S. military has achieved gains in the effort to recapture the Sunni city of Faluja, long regarded as the center of anti-U.S. unrest in Iraq. They said the marines have encountered moderate opposition and that 25 percent of Faluja has been captured.

The officials said the military has used the Iraqi Civil Defense Corps to help negotiate a surrender of Faluja as well as that of key Sunni insurgents. On Friday, Coalition Provisional Authority administrator Paul Bremer announced a 24-hour ceasefire to allow for mediation by an Islamic party to end the insurgency.