As around 200 U.S. forces made their first deployment into the holy Shiite city of Najaf (search), troops killed 64 insurgent gunmen and destroyed an anti-aircraft system in the area, U.S. military officials said Tuesday.

An American soldier was also killed Tuesday in Baghdad, raising the U.S. death toll for April to 115 — the same number lost during the entire invasion of Iraq last year.

U.S. troops were backed by helicopter gunships during the Najaf fighting, which lasted several hours, a military spokesman said.

Night television news footage — taken from a road between Najaf and the nearby town of Kufa —showed U.S. Army helicopters flying low over plumes of smoke rising from a green area and the sparks of flashes, likely from gunfire.

The fighting came as U.S. troops moved into a base that Spanish troops are vacating, about three miles from holy shrines near where anti-American Shiite Muslim cleric Muqtada al-Sadr (search) is holed up.

U.S. commanders have said they will not move against the shrines in order to capture al-Sadr, whose armed supporters have launched attacks against the U.S.-led forces. Under the Geneva Conventions (search), it's prohibited to fire upon mosques or other holy sites unless the structures are being used in battle.

Enemy forces in Fallujah and elsewhere have been using holy sites as shelter as they fire upon the U.S. military.

Attempts to capture al-Sadr have been put on hold while negotiators try to resolve the standoff. The Americans say they're aware that moving against the shrines could turn the cleric's limited revolt into a wider anti-U.S. uprising by Iraq's Shiite majority.

The battles in the south Monday evening took place on the east side of the Euphrates River, across from Kufa and Najaf, Brig. Gen. Mark Kimmitt said.

The first fight came in the afternoon, when Shiite militiamen opened fire on a U.S. patrol. In the ensuing firefight, seven insurgents were killed. Hours later, a M1 tank was attacked with rocket-propelled grenades. A heavy battle erupted, during which warplanes destroyed an anti-aircraft gun belonging to the militia and 57 gunmen were killed, Kimmitt said.

Kimmitt told Fox News Tuesday that insurgents in Najaf number in the "hundreds, certainly not thousands" and that the reason more Iraqis are not turning them in is that they are afraid of them.

"I think most of it has to do with the fact that the citizens have been intimidated for years and years … that's probably the reason that they're [enemy fighters] not being expelled by their own people," Kimmitt said.

When asked if the U.S.-led coalition can get rid of enough guerillas to decrease the terror threat, Kimmitt said yes, adding that, "we certainly have done that to Sadr's militia."

"We've taken some decisive military operationss against them, we've reduced them in almost all the locations where they tried to hijack the [democratic] process … the media networks, the gvovernment buildings; we're gonna cont to hunt down these Sadr miltaria types until they're no longer a threat to Iraq," Kimmitt continued.

Also Tuesday, a Red Cross team visited Saddam Hussein to see his conditions in U.S. custody, Kimmitt said, but he refused to say where the visit took place. It was the first since the Red Cross visited the ousted Iraqi leader in February.

June 30 Deadline Looms

Meanwhile, as the United Nations prepared to discuss the formation of a caretaker government due to take power on June 30, U.S.-appointed Iraqi leaders complained that the administration will not have real sovereignty — promised by American administrators — for months.

"I think the sovereignty will be weak and not complete," said Mahmoud Othman, a member of the Iraqi Governing Council. For "the security situation, there will still be the United States."

He also expressed worry that the caretaker will be limited in what laws it can pass. If the government can't make laws or provide security, "it will not be real sovereignty," he said. "The less sovereignty there is, the less the possibility that the government will be able to work and achieve its tasks."

U.N. envoy Lakhdar Brahimi has proposed that the Governing Council be dissolved and a caretaker government be created to run Iraq from June 30 until January elections. The United States has said that since Iraqi security forces are still not up to the task of fighting insurgents, U.S. forces will hold security powers even after the handover.

But U.S. officials assured everyone that soverignty will be turned over the Iraqis but issued a reminder that coalition troops will remain in Iraq until the country is secure.

"We've said all along that Iraqis will get sovereignty on June 30," Dan Senor, spokesman for U.S. civilian administrator Paul Bremer, told Fox News. "It is as much central to our security strategy as anything else."

But Senor said to keep in mind that "Iraq will not be in a position to defend against what we believe to be the significant terror threat that will be here after June 30. That's why coalition forces must stay until Iraqi forces can defend themselves."

Talks in Fallujah

On Monday, U.S. troops came under heavy attack in Fallujah (search), a day after U.S. officials decided to extend a cease-fire rather than launch a full-scale offensive on that city. Eight suspected insurgents and one U.S. Marine were killed.

Military officials were hopeful that talks between city leaders and insurgent groups were making progress and that another offensive would not have to be launched.

"The Marines on the ground seem to be quite pleased with the way things are going there" in Fallujah, told Fox News on Tuesday. "I think the sense on the ground is, as long as we're making progress, let's see if this political track can work."

Meanwhile, a workshop in Baghdad believed to be producing chemical munitions exploded in flames moments after U.S. troops broke in to search it on Monday. Two American soldiers were killed and five wounded. Jubilant Iraqis swarmed over the Americans' charred Humvees, waving looted machine guns, a bandolier and a helmet.

The deaths of the two soldiers in Baghdad and the Marine in Fallujah brought to 114 the number of U.S. troops killed in combat so far this month — nearly as many as the 115 Americans killed during the invasion that toppled Saddam.

The Associated Press contributed to this report.