A U.S. military official says U.S. troops will move back to the "periphery" of sensitive areas, says CBS News Reporter Charles D'Agata.
The announcement by Gov. Adnan al-Zurufi came one day after aides to radical cleric Muqtada al-Sadr said they would begin removing their fighters from the cities, although there was no sign of any such movement by late afternoon.
The move is aimed at ending a two-month armed standoff between the Americans and al-Sadr's al-Mahdi Army in the two cities, which contain some of the most sacred shrines in Shia Islam.
"All fighting forces, the coalition forces and the al-Mahdi Army militia, should leave the two holy cities and not allow any of their elements to enter again," al-Zurufi said.
The governor said the withdrawal order takes effect at 6 p.m. local time, after which the Iraqi police will assume full responsibility for security in the two cities.
But even as the reports of a pullout from Najaf and Kufa emerged, al-Sadr criticized the new Iraqi government and said he would accept "nothing less" than an elected leadership, and his militia fighters battled American soldiers in a teeming Baghdad district.
A truce in Najaf and Kufa has already all but collapsed.
In other developments:
Standing next to Prime Minister John Howard after the pair held talks in Washington early Thursday, Mr. Bush said it would be "a disastrous decision for the leader of a great country like Australia to say, 'We are pulling out."'
Political analysts said Mr. Bush's attack could politically damage Howard, who has made his government's strong security and trade ties with Washington a centerpiece of his foreign policy.
In Baghdad, unknown gunmen attacked a U.S. Army patrol on Palestine street near the Shiite district of Sadr City, and the 1st Cavalry Division said four soldiers were wounded.
Shiite insurgents fired mortar rounds and rocket-propelled grenades at a police station housing U.S. troops, touching off firefights early Friday that killed three Iraqis.
Helicopters and jet fighters flew over the station during the exchanges that the insurgents say came after U.S. troops tried to raid homes and arrest militiamen. A mortar round killed two militiamen and a civilian, said one al-Sadr official who spoke on condition of anonymity.
"This is the democracy George Bush brought us," shouted one young boy as he displayed a blanket that was burned and tattered in the exchanges. Crowds of irate teens gathered around, including one child that showed off his handgun to television news crews.
Al-Sadr failed to appear Friday for Muslim prayers in the mosque in Kufa where he routinely preaches, but instead sent an aide, Jaber al-Khafaji, to deliver his sermon on his behalf.
"America has taken upon itself to appoint a prime minister and a president of the nation under the cover of the United Nations," al-Sadr said in the message. "It has done that with impertinence and domination. The government must be elected and I will never accept anything beneath that."
He said he could not imagine "any reasonable person would ever accept" a government "which comes from no less than the occupying power."
Al-Sadr launched his uprising in April after the U.S.-led coalition shut down his newspaper, arrested a top aide and announced an arrest warrant charging him with murder in the April 2003 death of a moderate cleric in Najaf.
A more influential Shiite cleric, Grand Ayatollah Ali al-Husseini al-Sistani, has given a conditional endorsement to the new administration announced Tuesday by U.N. envoy Lakhdar Brahimi. Al-Sistani said the government would have to win the trust of the people by regaining genuine sovereignty, restoring security, preparing for elections by Jan. 31 and relieving the suffering of the Iraqi public.