BAGHDAD — U.S. and Iraqi forces began major military operations today north and south of Baghdad, while Iraqi officials said 36 people were killed in clashes in southern Iraq.

An official in the office of Iraq's national security adviser confirmed the operations, which were also launched in the Tharthar area near Fallujah and in Diyala province.

Iraqi security forces were in the lead, backed by U.S. forces, the official said on condition of anonymity for security reasons. He refused to estimate the number of troops involved, or how long the operations would last.

Meanwhile, Iraqi and British forces fought a fierce battle with Shiite militiamen while conducting house-to-house searches early today in and around Amarah, 200 miles southeast of Baghdad. It was unclear whether the fighting was part of the new military operations.

A doctor at Amarah's general hospital said 36 bodies had been taken to his facility, though he could not determine how many were militiamen and how many were civilians. He spoke on condition of anonymity because he was not authorized to talk to media.

More than 100 people were injured in the fighting, and at least three of those killed were Iraqi policemen, police and hospital officials said.

The U.S. military released a statement saying at least 20 insurgents had been killed and six wounded in coalition operations targeting "secret cells" in Amarah. Another suspect was detained, it said.

The men were believed to be members of a terrorist network that imports deadly armor-piercing weapons made in Iran known as "explosively formed penetrators," or EFPs, the statement said. They also were suspected of bringing militants from Iraq to Iran for terror training, it added.

Coalition forces came under small arms fire and rocket-propelled grenade attacks in the raids and called in air support, the military said. The suspects were killed by fire from aircraft, it said.

The U.S. statement did not specify whether the coalition troops were American or British.

Iraqi police said the Mahdi Army, the militia commanded by radical Shiite cleric Muqtada al-Sadr, was involved in the clashes, which lasted for about two hours before dawn.

Amarah is the provincial capital of Maysan province, a predominantly Shiite region that borders Iran. Iraqi forces took over control of security from British troops there in April.

Elsewhere Monday, eight people were killed in clashes that erupted between Iraqi police and Mahdi Army fighters in Nasiriyah, about 70 miles south of Amarah, police said. More than 60 people were injured, most of them police, they said.

The fighting began after some police patrols were attacked there Sunday night, officials said.

Some local tribesman had joined the fight, siding with Iraqi police in trying to oust the militiamen from their town, the officials said.

The battle included at least 11 mortar strikes on Nasiriyah police headquarters.

Clashes continued through today, and authorities imposed an indefinite curfew on the city, police said. By early afternoon, the fighting had spilled over into the Souk al-Sheikh area south of Nasiriyah.