BAGHDAD, Iraq — Prime Minister al-Maliki gave Shiite Muslim militiamen in Basra three days to surrender as fighting raged yesterday in the southern Shiite heartland and parts of Baghdad, leaving more than 80 people dead since the previous day.

Basra residents trapped in their homes by raging gun-battles worried that food was running out with no end in sight to the clashes between Iraqi security forces, followers of a radical Shiite cleric, Moqtada al-Sadr, and other armed factions.

Volleys of rocket and mortar fire shook the capital yesterday, including the fortified Green Zone, which houses the American Embassy and Iraqi government offices. One U.S. soldier, two American civilians, and an Iraqi soldier were wounded in the attacks, the military said.

Two American soldiers were killed by hostile fire in separate attacks yesterday in Baghdad, the military said without naming the assailants. The deaths lifted to at least 4,002 the number of American personnel killed since the start of the American-led invasion of Iraq in March 2003, according to the independent Web site icasualties.org.

Fighting erupted Tuesday in Basra when Iraqi government security forces announced the launch of a crackdown against armed factions and criminal gangs that are vying for control of the city and its lucrative oil industry. By yesterday, more than 30 people had been killed and 100 injured in Iraq’s second largest city, health officials said.

The level of resistance represented a major challenge to Mr. Maliki’s authority and deepened fears that a cease-fire declared last year by Mr. Sadr might be in danger of collapse. The truce has played a key part in the significant drop in violence since an American troop buildup reached its peak in June.

Mr. Sadr’s followers have charged for months that American and Iraqi security forces, many of them with ties to rival Shiite factions within the government, are taking advantage of the truce to arrest members of Mr. Sadr’s Mahdi Army militia and weaken his movement ahead of provincial elections slated for October 1. Mr. Sadr’s representatives called Tuesday for nationwide protests in response to the latest crackdown.

The unrest quickly spread to Kut, Hillah, and several neighborhoods of Baghdad, where small groups of demonstrators took to the streets and members of the Mahdi Army traded gunfire with American and Iraqi security forces and rival militias. Late yesterday, explosions could also be heard in the Shiite holy city of Najaf.