DIWANIYAH, Iraq (AP) – The fighting lasted through the night and most of Monday, with more and more Iraqi troops moving in to try to put down a Shiite militia. By the end of the battle, the militia controlled a large swath of this southern city, and 40 people were dead.

The first major skirmish between the military and militiamen made lethally clear how difficult it will be for Iraq’s Shiite-led government to rein in the violent sectarian forces of a radical cleric.

The fighting in this southern city dominated a day that saw at least 19 people die in two suicide car bombings in Baghdad – one outside the Interior Ministry and one on a line of cars waiting for fuel at a gas station.

The U.S. military announced that nine U.S. soldiers were killed over the weekend in and around Baghdad, eight of them by roadside bombs and one by gunfire.

Still, U.S. military authorities said there was less violence than before.

“We have reduced the amount of violence,” U.S. military spokesman Maj. Gen. William B. Caldwell told reporters in Baghdad. “We are actually seeing progress out there.”

“Whether it is shops opening, banks opening, neighborhood trash being removed, women and children moving about in their neighborhoods … Iraqi security forces are making progress,” he said.

Diwaniyah, 80 miles south of Baghdad, is a Shiite-dominated city where the influence of firebrand cleric Muqtada al-Sadr’s Mahdi Army has been gradually increasing. The militia of the Mahdi Army already runs a virtual parallel government in Sadr City, a slum in eastern Baghdad.

But the government of Prime Minister Nouri al-Maliki, a Shiite, has found it difficult to rein in al-Sadr, whose movement holds 30 of the 275 seats in parliament and five Cabinet posts. Al-Sadr’s backing also helped al-Maliki win the top job during painstaking negotiations within the Shiite alliance that led to the ouster of Prime Minister Ibrahim al-Jaafari.

Many Sunnis have expressed disappointment that al-Maliki’s government has not moved to curb Shiite militias, especially the Mahdi Army. A prominent hardline Iraqi Sunni cleric said Friday he was willing to meet with top Shiite religious leaders, part of an initiative to curb sectarian violence – but also to press Shiite leaders into a response.

American forces also have been wary of confronting the militia, because of al-Sadr’s clout over the government and his large following among majority Shiites. Al-Sadr mounted two major uprisings against the American-led coalition in 2004 when U.S. authorities closed his newspaper and pushed an Iraqi judge into issuing an arrest warrant against him.

The clashes in Diwaniyah began Saturday night after a rocket attack on a Polish-run base earlier in the day, and then resumed Sunday night, said Lt. Col. Dariusz Kacperczyk, a Polish military spokesman.

Sheikh Abdul-Razaq al-Nidawi, the manager of al-Sadr’s office in Diwaniyah, told The Associated Press that trouble had been brewing since Saturday night when the army arrested an al-Sadr supporter from the Jumhouri neighborhood.

On Sunday, the army raided the same place and “a gunfight erupted between them and the Mahdi Army,” al-Nidawi said.

Army Capt. Fatik Aied said gunbattles broke out at about 11 p.m. Sunday south of Diwaniyah, when Iraqi soldiers conducted raids in three neighborhoods to flush out militiamen and seize weapons.

Al-Nidawi said “a big force of the army raided Jumhouri, Sadr and Askouri neighborhoods and clashes broke out (again) between the army and the Mahdi Army.” He said the raids took place early Monday.

The U.S.-led military command in Baghdad said trouble began at about midnight on Sunday when Iraqi police and soldiers went to check on reports of a gathering in the city.

Fighting continued for most of the day, as the army brought in extra troops from other cities to reinforce its soldiers, said Brig. Gen. Othman al-Farhoud, commander of the 8th Iraqi Army Division.

By evening, the militia had set up road checkpoints and taken over seven neighborhoods in the south and east of the city, while the Iraqi army was controlling the northern and western parts, said Capt. Aied of the Iraqi army.

The U.S.-led military command said in its statement that the Iraqi army and police “successfully fended off an attack by a large group of terrorists” in three districts of Diwaniyah after a 12-hour battle.

Dr. Mohammed Abdul-Muhsen of the city’s general hospital said 40 people had been killed – 25 Iraqi soldiers, 10 civilians and five militiamen. He said the hospital treated 75 wounded, but could not immediately give a breakdown.

Aied said the militiamen used rocket propelled-grenades and automatic assault rifles, and that at least 10 militiamen were arrested.

An indefinite vehicle ban was imposed in the city, said Adnan Abdu-Kadhim, a member of the provincial council.

Coalition forces were not involved in the fighting, but provided support with an aerial quick reaction force, using military helicopters as a show of force and to prevent possible attacks from rooftops, Kacperczyk said. Coalition quick reaction forces were also patrolling near the city, he said.

One Polish helicopter was hit by small arms fire but was able to land safely at the nearby base, the U.S.-led military command said.

In the capital, a suicide car bomber slammed into a police checkpoint outside the Interior Ministry. The blast could be heard more than one mile away, and smoke could be seen rising from the scene. The blast killed 16 people, including 10 policemen, Police 1st Lt. Ahmed Mohammed Ali said. He said 18 policemen were among the 47 people wounded.

Elsewhere in Baghdad, a suicide car bomber struck a queue of cars waiting at a gas station in the southern neighborhood of Dora, killing three civilians and wounding 15, Lt. Ahmed Hameed of the national police said.

Earlier in the day, a roadside bomb in the mainly Sunni western neighborhood of Jihad struck a car transporting five barber shop workers. One person was killed and another four were seriously wounded, police Lt. Maitham Abdul-Razzaq said.

Meanwhile, about 100 Iraqi Shiite soldiers refused to go to Baghdad to support the security crackdown there, marking the second time a block of Iraqi soldiers have balked at following their unit’s assignment, a U.S. general said Monday.

U.S. Brig. Gen. Dana Pittard, commander of the Iraqi Assistance Group, said the problems stem from the Iraqi Army’s regional divide, because soldiers are recruited in their home area and expect to train and serve there.