WASHINGTON -- A former general from Saddam Hussein's Republican Guard has not been given command of an Iraqi force that entered Fallujah after Marines ended a three-week siege, the U.S. military chief said Sunday.

Gen. Richard Myers said news media were "very, very inaccurate" in their reporting about Maj. Gen. Jassim Mohammed Saleh, who was said to have had a major role in organizing the "Fallujah Brigade" and the lifting of the siege.

Myers, chairman of the Joint Chiefs of Staff, said officials in Baghdad were checking into Saleh's background.

"There are people that know his record, know what he's done in the previous Saddam Hussein regime," Myers said on CBS' "Face the Nation."

"They're going to have to find an appropriate role, if a role at all, for him," Myers said.

On "Fox News Sunday," Myers said: "He has not been vetted yet and probably won't be the one in command."

The secretary-general of the United Nations, Kofi Annan, agreed that "those who've committed crimes have no business getting involved" in the Iraqi people's security forces.

But "you had people in the army -- this was a large army, I don't think all of them committed atrocities, but most of the leadership is gone," Annan told NBC's "Meet the Press." "But those who are clean, I think, can be used."

In Iraq, Saleh's friends and relatives said he served in the Republican Guard in the 1980s and later headed Saddam's infantry forces. Nevertheless, Marine commanders have given no indication they are losing confidence in the general, whom they describe to reporters as commander of the Fallujah force.

On Sunday, Marine Lt. Col. Brennan Byrne told reporters near Fallujah that Saleh had opposed Saddam's regime and paid a "steep personal price."

Byrne and his colleagues appear to have accepted Saleh because he offered the best alternative to bloody fighting that could have produced casualty rates politically untenable both in Iraq and the United States.

The Marines backed off their threatening posture around Fallujah, inhabited by adherents of deposed President Saddam's Sunni branch of Islam, as elements of Saleh's "Fallujah Brigade" replaced them Saturday. In the city, crowds waved Iraqi flags, cheered and celebrated, many flashing "V" for victory signs.

Whatever the disposition of Saleh, Myers said, "We want Iraqis to do this work, and this is a microcosm of what we want to happen all over Iraq."

He said the original objectives in Fallujah remained:

--"Deal with the extremists, the foreign fighters."

--"Get rid of the heavy weapons out of Fallujah."

--"Find the folks who perpetrated the Blackwater atrocities."

The siege began after four civilian security personnel from the North Carolina-based Blackwater Security Consulting were attacked, killed and burned and mutilated.

"The reports that the Marines have pulled back, not true. The Marines are still where they've been," Myers said. "The Marines are prepared to follow through on this action if they have to."

But, he said, "We think this is far preferable than the U.S. going in there in a very major combat operation to achieve those objectives. If we can do it with Iraqis, that is preferable."

Sen. John McCain, second-ranking Republican on the Senate Armed Services Committee, found considerable fault with the outcome so far in Fallujah. McCain, a naval aviator in the Vietnam War who spent 5.5 years as a prisoner of war, said the U.S. military has made too many threats without following through.

"The perception right now is that we are not acting in a decisive fashion and there's no greater mistake you can make in the conduct of warfare," he told ABC's "This Week."

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