The US military said on Sunday the soldiers were killed while patrolling the capital in search of weapons and bomb-making materials.
A soldier from the 13th Sustainment Command was killed and two were wounded when a blast struck their vehicle on Saturday near the city Diwaniyah, the command said.
The Ramadi suicide bombing occurred on Sunday morning, about 115km west of Baghdad.
Police said they were suspicious of the truck and opened fire as it approached their checkpoint.
The bomber then detonated the explosives.
Separately, US forces located Azhar al-Dulaimi in northern Baghdad on Friday morning and tried to capture him, but he was killed in the ensuing battle, Major-General William Caldwell, the spokesman for the US-led forces in Iraq, said.
The Shia fighter is believed to have been the mastermind of the January 20 attack in Karbala where fighters speaking English, wearing US military uniforms and carrying American weapons attacked a joint military command headquarters where US and Iraq officers were meeting.
The attackers killed one soldier and abducted four others, whom they later shot to death.
News of al-Dulaimi's death came as thousands of soldiers continued searching for three of their comrades who were captured in an ambush south of Baghdad last week that also killed four other soldiers and their Iraqi interpreter.
Increased US patrols as part of the new Baghdad security plan to regain control of the capital have resulted in a spike in military casualties over the past few months.
At least 15 US servicemen have been reported killed just this weekend and 76 so far this month, putting May on track to be one of the bloodiest months in the four-year-old conflict for the Americans.
The deaths bring the total US casualty toll since the March 2003 US-led invasion to 3,419 according to an AFP count based on Pentagon figures.