BAGHDAD, Iraq, (AP) – Lawmakers across party lines on Tuesday endorsed the prime minister’s new plan for stopping sectarian killings, but Shiite and Sunni leaders still had to work out details of how to put aside their sharp divisions and work together to halt the violence.

At least 33 people were killed in violence around Iraq, including a suicide attack on a fish market in Baghdad that killed three people and wounded 19. A bomber detonated a belt rigged with explosives in the outdoor market in the primarily Sunni area of Sadiyah in southwestern Baghdad, police Lt. Maitham Abdul Razzaq said.

Meanwhile, the U.S. command announced the deaths of nine soldiers and two Marines over the past few days.

Four of the soldiers were killed in Baghdad on Monday in separate small-arms fire attacks, the military said. Another four were killed the same day in a roadside bomb attack on their patrol northwest of Baghdad at 6 p.m. (1500 GMT)

The ninth died Sunday when his vehicle was struck by a roadside bomb west of the capital.

The two Marines, both with the Regimental Combat Team 7, were killed in fighting in the western Anbar province, one on Sept. 30 and one on Oct. 1, the military said.

The government of Prime Minister Nouri al-Maliki has been under intense pressure to put an end to Shiite-Sunni violence that has killed thousands of people this year. This week, gunmen carried out two mass kidnappings in as many days, snatching 38 people from their workplaces in Baghdad — attacks that Sunnis said were carried out by Shiite militias.

Monday night, al-Maliki announced a new four-point plan aimed at uniting the sharply divided Shiite and Sunni parties in his government behind security efforts to stop the bloodshed.

The parties have long been blaming each other for the killings.

Sunnis accuse the Shiite-led security forces of turning a blind eye to killing of Sunnis by Shiite militias — some of which are linked to parties in the government. Sunnis have accused al-Maliki, a Shiite, of being hesitant to crack down on the militias.

Shiites, meanwhile, accused Sunni parties of links to terrorists after a bodyguard of a Sunni party leader, Adnan al-Dulaimi, was arrested by U.S. forces on Friday and accused of plotting al-Qaida bombings.

The four-point plan, signed by all sides, aims to resolve disputes by giving every party a voice in how security forces operate against violence on a neighborhood by neighborhood level.

Local committees will be formed in each Baghdad district — made up of representatives of every party, religious and tribal leaders and security officials — to consult on security efforts. A Sunni representative, for example, could raise a complaint if he feels police are not pursuing a Shiite militia after an attack. A central committee, also made up of all the parties, will coordinate with the armed forces.

The top parties were to meet later Tuesday to work out details of how the committees will operate — a process that is rife with possible pitfalls.

They must work out how many members of each party will be on each committee and how much voice each member will have, what geographical areas the committees will cover, how decisions by the committees will be made.

The parties are so divided that even in talks Monday over the plan, they split over the terminology for the bloodshed that the committees seek to end: Shiites want the fight to be against “terrorism,” which would focus on Sunni insurgents, while Sunnis want it against “violence” — which would include killings by Shiite militias.

In parliament on Tuesday, lawmakers from Sunni, Shiite and Kurdish parties all hailed the new plan as a necessary step in the right direction.

“We do not want to blame this side or that side — there is a sectarian tension in which all have been a part,” said Hadi al-Amiri, a top Shiite lawmaker in al-Maliki’s governing coalition. “We have to take responsibility and be courageous to deal with this sectarian tension.”

But another lawmaker, Izzat Shabandar, from the secular Iraqi Bloc, cautioned that “we have to be realistic” — and he pointed to the role of militias run by members of the government.

“Those who signed this blessed agreement have to confess, at least to themselves, they are the basis of the problem and they are part of it. If they cannot confess that to themselves they will not be able to … be part of the solution,” he said.

Al-Maliki announced a 24-point reconciliation plan when he took office in May, which laid down ways to tackle violence — including an amnesty for militants who put down their weapons as well as security crackdowns. But so far, the plan has done little to stem the daily killings.

Demonstrators marched through the al-Amil neighborhood of western Baghdad protesting the Sunday night kidnapping of 24 workers from a factory producing frozen food.

Seven bodies found late Sunday in the predominantly Sunni neighborhood of Dora were identified as victims of the kidnapping, but the whereabouts of the others are still unknown.

Another 14 people, workers in computer shops, were seized on Monday by gunmen.

Around 400 demonstrators chanted “Sunnis and Shiites are brothers,” as they marched through the streets.

Some carried banners reading “get police troops out of our area” — reflecting the widespread suspicion that Iraqi security forces have been infiltrated by militias and are responsible for some of the sectarian violence.