Suspected Shi'ite extremists hammered the US-protected Green Zone Sunday in the fiercest salvo in weeks, apparently taking advantage of a sandstorm that blanketed the capital and grounded the American aircraft that normally prowl for launching teams. Thunderous explosions resounded throughout the evening as rockets or mortar shells slammed into the heavily fortified area in central Baghdad. Anti-US cleric Muqtada al-Sadr, meanwhile, rejected terms set by the Iraqi government for lifting a crackdown against his Mahdi Army militia - the latest in a series of often conflicting messages from the Shi'ite leader. Sirens wailed in the Green Zone, which houses the US Embassy and much of the Iraqi government on the west side of the Tigris River, and the public address system warned people to "duck and cover" and stay away from windows. The US Embassy confirmed the area was hit by indirect fire, the military's term for rocket or mortar attacks, but said it had no immediate word on casualties. The Green Zone has been regularly shelled since fighting broke out over a US-backed government crackdown against militias that began in late March. At least four Americans, including two soldiers, have been killed in the attacks. But the US military has claimed success with operations that have effectively sealed off the southern section of Baghdad's Sadr City, a militia stronghold that is believed to be one of the prime launching sites for the Green Zone attacks. "Security operations are still ongoing as criminal groups in some areas continue to challenge the government and the rule of law. However, operations of the last several weeks have been successful," US military spokesman Rear Adm. Patrick Driscoll said earlier Sunday at a news conference in the Green Zone. American commanders have blamed what they call Iranian-backed Shi'ite factions they say have broken with a cease-fire imposed by al-Sadr in late August. Al-Sadr's spokesman in the holy city of Najaf called the Shi'ite-led government's terms for stopping the crackdown against the militias "illogical." Salah al-Obeidi accused Prime Minister Nouri al-Maliki, himself a Shi'ite, of wanting to resolve the problem by force instead of dialogue. Chief among al-Maliki's demands announced Friday were that the militias surrender heavy weapons and hand over all wanted people. Sporadic clashes also continued Sunday in Sadr City, a sprawling district in northeastern Baghdad with 2.5 million people. The US military said five suspected militants were killed in three separate airstrikes late Saturday and early Sunday in the area. A local hospital official, speaking on condition of anonymity because he was not authorized to release the information, said one person was killed and 11 others wounded in street battles. In all, at least 349 Iraqis have been killed since the daily clashes began on March 25, 34 of them since Wednesday, according to an Interior Ministry official who declined to be identified for the same reason. Acknowledging the hardship caused by the crackdown for ordinary Iraqis in the densely packed district, a visiting delegation of about 40 lawmakers from various Sunni, Kurd, Turkomen and Shi'ite parties urged the government to stop the military campaign there. But Brig. Gen. Qassim al-Moussawi, the Iraqi military spokesman for Baghdad operations, refused to set an end date, saying it was an ongoing effort. Al-Moussawi also said that over the past month, militants had fired a total of 712 missiles and mortar rounds inside Baghdad. "They were all Iranian-made brought into Iraq in many ways," Brig. Gen. Qassim al-Moussawi told reporters at a joint news conference with Driscoll. He did not elaborate on how the security forces had determined the origin of the exploded munitions. Heavy clashes also broke out between Shi'ite militiamen and Iraqi troops in the Maalif area on the southwestern edge of Baghdad. Police said that five people died and 14 were wounded in the fighting. The US military said its forces were not involved. Associated Press Television News footage from the area showed a minibus riddled with bullets and a pool of blood in another minibus. Two suicide car bombers also targeted Iraqi forces elsewhere in Baghdad. One killed three people and wounded nine and another killed two and wounded five. In political developments, al-Maliki met with Sunni Vice President Tariq al-Hashemi to discuss rebuilding a "national and unified government," a statement from the president's office said. The meeting came amid a series of optimistic statements that the main Sunni bloc, the National Accordance Front, is ready to rejoin the Cabinet after a nearly nine-month absence. But Sunni officials have said internal power struggles within the Front over who should be appointed to which posts have delayed a formal decision. Northeast of Baghdad, Iraqi troops also unearthed a mass grave containing more than 50 decomposed bodies in an orchard in an area that had been controlled by al-Qaida in Iraq near Baqouba, according to the Diyala provincial coordination center.