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.