Suspected Shiite extremists also unleashed rockets or mortars against the U.S.-protected Green Zone in central Baghdad for the third day this week.
Three Americans were seriously injured in Wednesday's attacks, U.S. Embassy spokeswoman Mirembe Nantongo said. At least eight Iraqis also were killed after several mortar or rocket rounds apparently fell short in several areas in Baghdad, according to police and hospital officials.
The ultimatum came as Prime Minister Nouri al-Maliki remained in Basra to supervise a crackdown against the spiraling violence between militia factions vying for control of the center of the country's vast oil industry located near the Iranian border.
Basra has been largely run by militias, most notably the powerful Mahdi Army, controlled by radical Shiite cleric Muqtada al-Sadr, and getting any of them to voluntarily give up their arms was going to be a daunting task. "The prospects of that are very low," says CBS News reporter Phil Ittner.
At least 55 people were killed and 300 wounded in Basra and Baghdad in fighting that broke out Tuesday and spread to the capital's main Shiite district of Sadr City, according to Iraqi police and hospital officials.
"This has been a difficult and challenging few days," U.S. military spokesman Maj. Gen. Kevin Bergner said. "It has been a period of significant effort by the Iraqi government."
However, the White House called the fighting "the exact opposite" of a setback.
"This is exactly what we all want to see - which is the government of Iraq taking the initiative that was afforded to it by the surge to go aggressively after illegal criminal gangs" and militias in the Basra region," spokesman Tony Fratto told reporters Wednesday.
The violence has raised fears that the cease-fire declared in August by al-Sadr could unravel, presenting the gravest challenge to the Iraqi government in months.
Officials in al-Sadr's headquarters in Najaf, speaking on condition of anonymity because of the sensitivity of the issue, said the anti-U.S. cleric had sent local representatives to ask al-Maliki to leave Basra and to resolve the problems peacefully. The aides also told the government no negotiations could be held until Iraqi reinforcements withdrew from the city.
A resumption of intense fighting by his Mahdi Army militia could kill more U.S. soldiers and threaten - at least in the short run - the security gains Washington has hailed as a sign that Iraq is on the road to recovery.
CBS News chief foreign correspondent Lara Logan reports that two U.S. military convoys were attacked Tuesday night by Mahdi Army militiamen.
In an effort to win support, al-Sadr ordered his men to deliver the Holy Koran to Iraqi soldiers and police manning checkpoints - the gesture was apparently well received, says Logan.
The Sadrists are angry over recent raids and detentions, saying U.S. and Iraqi forces have taken advantage of the cease-fire to crack down on the movement.
They also have accused rival Shiite parties, which control Iraqi security forces, of engineering the arrests to prevent them from mounting an effective election campaign. The showdown with al-Sadr has been brewing for months but has accelerated since parliament agreed in February to hold provincial elections by the fall.
Bergner insisted the Sadrists weren't being singled out and blamed Iranian-backed rogue militia factions for the recent violence, although he declined to link Tehran directly to the fighting.
The military spokesman also noted the Iraqi government was taking the lead in the Basra operation, although U.S. troops were involved as members of transition teams helping train the Iraqis.
He said the Iraqi government had appealed to Iran to help restore calm in Basra.
"This is not a battle against the (Mahdi Army) nor is it a proxy war between the United States and Iran," he said. "It is the government of Iraq taking the necessary action to deal with criminals on the streets."
Tensions continued Wednesday in Basra, the center of the country's vast oil industry located near the Iranian border. Gunfire echoed through the streets as Iraqi soldiers and police fought the Mahdi Army, police said.
Reinforcements were sent to Iraq's second-largest city from the Shiite holy city of Karbala, Interior Ministry spokesman Maj. Gen. Abdul-Karim Khalaf said, adding a large number of gunmen have been detained.
Mortar rounds also hit a detention center in central Basra and injured 10, police said.
Sadiq al-Rikabi, a chief adviser to al-Maliki, said gunmen who fail to turn over their weapons to police stations in Basra by Friday will be targeted for arrest. He added that they also must sign a pledge renouncing violence.
"Any gunman who does not do that within these three days will be an outlaw," he said.
The burgeoning crisis - part of an intense power struggle among Shiite political factions - has major implications for the United States. It also will test the skill and resolve of Iraq's Shiite-led government in dealing with Shiite militias, with whom the national leadership had maintained close ties.
British troops have remained at their base at the airport outside Basra and were not involved in the ground fighting, although their planes were providing air surveillance, according to the British Ministry of Defense. It said Wednesday that the Iraqis had not asked it to intervene.
British forces turned over responsibility for Basra to the Iraqis in late December but say they will assist the Iraqis upon request.
Militia factions also have been fighting U.S. and Iraqi forces in Baghdad and other cities in reaction to the Basra crackdown.
Hundreds of al-Sadr supporters took to the streets Wednesday in Baghdad and Karbala, demanding the government stop military operations in Basra and withdraw all security forces.
"We strongly condemn the assaults being conducted by the occupation forces along with the Iraqi security forces who have sold themselves to the renegade occupier," said Sheik Saleh al-Eraibi, who was leading a demonstration in Sadr City.
Nobody claimed responsibility for the attacks against the Green Zone, which houses the American and British embassies as well as the Iraqi government headquarters.
Two rockets struck the parking lot of the Iraqi Cabinet, but no casualties were reported, an Iraqi security official said, speaking on condition of anonymity because he wasn't authorized to release the information.
The U.S. spokesman blamed Iranian-backed Shiite militia factions, saying most of the rockets had been fired from predominantly Shiite areas in eastern Baghdad, particularly Sadr City.
An American financial analyst working for the embassy was killed in a rocket attack on Sunday. Another volley slammed into the area on Tuesday, but no deaths or major casualties were reported
Bergner played down concerns that clashes with Shiite extremists could distract from the fight against al Qaeda in Iraq, saying the Sunni-led terror network remains the No. 1 threat to stability in Iraq.
"We have said all along that the security challenge facing Iraq is very much a mosaic," Bergner said. "We have consistently operated against that mosaic."